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Publications


Books 
[1] B.Kaltenbacher, A.Neubauer, and O.Scherzer.
Iterative Regularization Methods for Nonlinear Problems.
de Gruyter, Berlin, New York, 2008.

[2] T. Schuster, B. Kaltenbacher, B. Hofmann, and K. Kazimierski.
Regularization Methods in Banach Spaces.
de Gruyter, Berlin, New York, 2012.

[3] B. Kaltenbacher, I. Kukavica, I. Lasiecka, R. Triggiani, A. Tuffaha, J.T. Webster.
Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions Springer, Birkhäuser Mathematics, Oberwolfach Seminars, 2018.

[4] B. Kaltenbacher and W. Rundell.
Inverse Problems for Fractional Partial Differential Equations Number 230 in Graduate Studies in Mathematics. AMS.


Edited Volumes  
[1] T. Schuster, B. Hofmann, B.Kaltenbacher.
Special Issue on Tackling Inverse Problems in a Banach Space Environment.
Inverse Problems 28(10), 2012.

[2] L. Bociu, B. Kaltenbacher, P. Radu.
Special Volume on Nonlinear PDEs and Control Theory with Applications.
Evolution Equations and Control Theory EECT 2(2), 2013.

[3] P. Jordan and B. Kaltenbacher.
EECT Special Volume: Mathematics of nonlinear acoustics: New approaches in analysis and modeling.
American Institute of Mathematical Sciences AIMS, Springfield, US, 2016. Evolution Equations and Control Theory EECT 5.

[4] P. Jordan and B. Kaltenbacher.
EECT Special Volume: Nonlinear wave phenomena in continuum physics: some recent findings.
American Institute of Mathematical Sciences AIMS, Springfield, US, 2019. Evolution Equations and Control Theory EECT 8.

[5] C. Clason and B. Kaltenbacher.
Special Issue on Optimal Control and Inverse Problems.
Inverse Problems 35-36, 2019-20.

[6] B. Kaltenbacher, Th. Schuster, and A. Wald.
Time-dependent Problems in Imaging and Parameter Identification.
Springer Nature, Switzerland, 2021. ISBN 978-3-030-57784-1.



Book Chapters
[1] B.Kaltenbacher and M.Kaltenbacher.
Modelling and iterative identification of hysteresis via Preisach operators in PDEs.
In J.Kraus and U.Langer, editors, Lectures on Advanced Computational Methods in Mechanics,
volume 1 of Radon Series on Computational and Applied Mathematics, pages 1--50, Berlin, 2007. de Gruyter.

[2] M. Burger, B. Kaltenbacher, and A. Neubauer.
Iterative Solution Methods.
In O.Scherzer, editor, Handbook of Mathematical Methods in Imaging Springer, Science+Business Media, 2011.

[3] B. Kaltenbacher and M. Kaltenbacher.
Modeling and Numerical Simulation of Ferroelectric Material Behavior Using Hysteresis Operators.
In: Micka¨el Lallart, ed., Ferroelectrics - Characterization and Modeling,  2011. ISBN: 978-953-307-455-9.

[4] P. Steinhorst and B. Kaltenbacher.
Application of the Reciprocity Principle for the Determination of Planar Cracks in Piezoelectric Material.
in: Apel, Thomas; Steinbach, Olaf (Eds.), Advanced Finite Element Methods and Applications. Lecture Notes in Applied and Computational Mechanics, Vol. 66, Springer, 2013


Refereed Journal and Proceedings Papers

[1] B. Kaltenbacher (Blaschke), H.W. Engl, W. Grever, and M. Klibanov.
An appication of Tikhonov regularization to phase retrieval.
Nonlinear World, 3:771-786, 1996.

[2] B. Kaltenbacher (Blaschke), A. Neubauer, and O. Scherzer.
On convergence rates for the iteratively regularized Gauss-Newton method.
IMA Journal of Numerical Analysis, 17:421- 436, 1997.

[3] B. Kaltenbacher (Blaschke), and H.W Engl
Regularization methods for nonlinear ill-posed problems with applications to phase reconstruction
In H.W. Engl, A.K. Louis, W.Rundell, Eds., Inverse Problems in Medical Imaging and Nondestructive Testing. Springer, Wien-New York, 1997.  (Oberwolfach Workshop, 1996)

[4] B. Kaltenbacher.
Some Newton type methods for the regularization of nonlinear ill-posed problems.
Inverse Problems, 13:729-753, 1997.

[5] B. Kaltenbacher.
A posteriori parameter choice strategies for some Newton type methods for the regularization of nonlinear ill-posed problems.
Numerische Mathematik, 79:501-528, 1998.

[6] B. Kaltenbacher.
On Broyden's method for nonlinear ill-posed problems.
Numerical Functional Analysis and Optimization, 19:807-833, 1998.

[7] B. Kaltenbacher.
On convergence rates of some iterative regularization methods for an inverse problem for a nonlinear parabolic equation connected with continuous casting of steel.
Journal of Inverse and Ill-Posed Problems, 7:145-164, 1999.

[8] B. Kaltenbacher.
A projection-regularized Newton method for nonlinear ill-posed problems and its application to parameter identification problems with finite element discretization.
SIAM J.Numer.Anal., 37:1885-1908, 2000.

[9] B. Kaltenbacher.
Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems.
Inverse Problems, 16:1523-1539, 2000.

[10] B. Kaltenbacher.
On the regularizing properties of a full multigrid method for ill-posed problems.
Inverse Problems, 17:767-788, 2001.

[11] B. Kaltenbacher and J. Schöberl.
A saddle point variational formulation for projection-regularized parameter identification.
Numerische Mathematik, 91:675-697, 2002. DOI 10.1007/s002110100350.

[12] B. Kaltenbacher, A. Neubauer, and A.G. Ramm.
Convergence rates of the continuous regularized Gauss-Newton method.
Journal of Inverse and Ill-posed Problems, 10:261-280, 2002.

[13] B. Kaltenbacher and J. Schicho.
A multi-grid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems.
Numerische Mathematik, 93:77-107, 2002. DOI 10.1007/s002110100375.

[14] B. Kaltenbacher.
V-cycle convergence of some multigrid methods for ill-posed problems.
Mathematics of Computation, 72:1711-1730, 2003.

[15] H. Benameur and B. Kaltenbacher.
Regularization of parameter estimation by adaptive discretization using refinement and coarsening indicators.
Journal of Inverse and Ill-Posed Problems, 10:561-584, 2002.

[16] B. Kaltenbacher, M. Kaltenbacher, and S. Reitzinger.
Identification of nonlinear B-H curves based on magnetic field computations and multigrid methods for ill-posed problems.
European Journal of Applied Mathematics, 14:15-38, 2003.

[17] G. Bodnar, P. Pau, J. Schicho, and B. Kaltenbacher
Exact real computation in computer algebra
In F. Winkler and U.Langer, eds., Lecture Notes in Computer Science. Springer, 2003 (Proceedings of the SNCS'01)

[18] B. Kaltenbacher
Identification of nonlinear parameters in hyperbolic PDEs, with application to piezoelectricity
In K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch, Hrsg., Optimal Control of Coupled Systems of PDEs. Springer, 2006.
(Oberwolfach Workshop, 2005)

[19] M. Burger and B. Kaltenbacher.
Regularizing Newton-Kaczmarz methods for nonlinear ill- posed problems.
SIAM J.Numer.Anal., 44:153-182, 2006.

[20] B. Kaltenbacher.
Determination of parameters in nonlinear hyperbolic PDEs via a multiharmonic formulation, used in piezoelectric material characterization.
Math. Meth. Mod. Appl. Sci. (M3AS), 16:869-895, 2006.

[21] B. Kaltenbacher, T. Lahmer, M. Mohr, and M. Kaltenbacher.
PDE based determination of piezoelectric material tensors.
European Journal of Applied Mathematics, 17:383-416, 2006.

[22] B. Kaltenbacher.
Towards global convergence for strongly nonlinear ill-posed problems via a regularizing multilevel approach.
Numerical Functional Analysis and Optimization, 27:637-665, 2006.

[23] B. Kaltenbacher and A. Neubauer.
Convergence of projected iterative regularization methods for nonlinear problems with smooth solutions.
Inverse Problems, 22:1105-1119, 2006.

[24] B. Kaltenbacher.
Regularization by truncated Cholesky factorization: A comparison of four different approaches.
Journal of Complexity, 23:225-244, 2007.

[25] B. Kaltenbacher, T. Lahmer, and V. Schulz.
Optimal measurement selection for piezoelectric material tensor identification.
Inverse Problems in Science and Engineering, 16:369-387, 2008.

[26] B. Hofmann, B. Kaltenbacher, C. Pöschl, and O. Scherzer.
A Convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators.
Inverse Problems, 23:987-1010, 2007.

[27] B. Kaltenbacher.
A note on logarithmic convergence rates for nonlinear Tikhonov regularization.
Journal of Inverse and Ill-Posed Problems, 16:79-88, 2008.

[28] B. Kaltenbacher.
Identification of hystersis in Maxwell's equations.
COMPEL, 26:306-316, 2007. (special issue, OIPE, Sorrento, Sep. 2006).

[29] B. Kaltenbacher and M. Klibanov.
An inverse problem for a nonlinear parabolic equation with applications in population dynamics and magnetics.
SIAM Journal of Mathematical Analysis, 39:1863, 2008.

[30] B. Kaltenbacher and A. Lorenzi.
A uniqueness result for a nonlinear hyperbolic equation.
Applicable Analysis, 86:1397 - 1427, 2007.

[31] B. Kaltenbacher.
Convergence rates of a multilevel method for the regularization of nonlinear ill-posed problems.
Journal of Integral Equations and Applications, 20:201-228, 2008

[32] T. Hegewald, B. Kaltenbacher, M. Kaltenbacher, and R. Lerch.
Efficient modeling of ferro- electric behaviour for the analysis of piezoceramic actuators.
Journal of Intelligent Material Systems and Structures, 2008. doi:10.1177/1045389X07083608.

[33] T. Lahmer, M. Kaltenbacher, B. Kaltenbacher, and R. Lerch.
FEM based determination of real and complex elastic, dielectric and piezoelectric moduli in piezoceramic materials.
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 5:465-475, 2008.

[34] A. Griesbaum, B. Kaltenbacher, and B. Vexler.
Efficient computation of the Tikhonov regularization parameter by goal oriented adaptive discretization.
Inverse Problems, 24, 2008.

[35] G. Nakamura, M. Watanabe, and B. Kaltenbacher.
On the identification of a coeffcient function in a nonlinear wave equation. 2008. Inverse Problems 25 (2009), 035007.

[36] C. Clason, B. Kaltenbacher, and S. Veljović.
Boundary optimal control of the Westervelt and the Kuznetsov equation. Journal of Mathematical Analysis and Applications 356 (2009) 738--751, doi:10.1016/j.jmaa.2009.03.043.
see also: Tech. Rep. SFB-2008-013, SFB Research Center Mathematical Optimization and Applications in Biomedical Sciences, University of Graz (October 2008)

[37] B. Kaltenbacher and I. Lasiecka.
Global existence and exponential decay rates for the Westervelt equation.
Discrete and Continuous Dynamical Systems (DCDS), Series S, vol 2, pp 503-525, 2009.

[38] B. Kaltenbacher and S. Veljović.
Sensitivity analysis of linear and nonlinear lithotripter mo- dels.
European Journal of Applied Mathematics, 22 (2010), pp. 21-43.
see also: Tech. Rep. IOC-21, International Doctorate Program Identification, Optimization and Control with Applications in Modern Technologies (October 2008).

[39] B. Kaltenbacher, F. Schoepfer, and Th. Schuster.
Convergence of some iterative methods for the regularization of nonlinear ill-posed problems in Banach spaces.
Inverse Problems 25 (2009) 065003 (19pp), doi:10.1088/0266-5611/25/6/065003.
see also: Stuttgarter Mathematische Berichte, 2008-005.

[40] B. Kaltenbacher.
Boundary observability and stabilization for Westervelt type wave equations.
Applied Mathematics and Optimization 62 (2010), pp. 381-410.

[41] D. Cassani, B. Kaltenbacher, and A. Lorenzi.
Direct and inverse problems related to MEMS devices.
Inverse Problems 25 (2009) 105002..

[42] J. Baumeister, B. Kaltenbacher, and A. Leitao.
On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations,
Inverse problems and imaging (IPI) 4 (2010), pp. 335-350.

[43] B. Kaltenbacher.
A convergence analysis of the midpoint rule for first kind Volterra integral equations with noisy data.
Journal of Integral Equations (special issue Ch.W.Groetsch), 22 (2010), pp 313-340.

[44] M. Kaltenbacher, B. Kaltenbacher, T. Hegewald, and R. Lerch.
Enhanced Finite Element Formulation for Ferroelectric Hysteresis of Piezoelectric Materials.
Journal of Intelligent Material Systems and Structures, 21 (2010), pp.773-785.

[45] B. Kaltenbacher and B. Hofmann.
Convergence Rates for the Iteratively Regularized Gauss-Newton Method in Banach Spaces
Inverse Problems 26 (2010) 035007.

[46] F. Wein, M. Kaltenbacher, B. Kaltenbacher, G. Leugering, E. Bänsch, and F. Schury,
On the Effect of Self-Penalization of Piezoelectric Composites in Topology Optimization,
Structural and Multidisciplinary Optimization , 2010, doi 10.1007/s00158-010-0570-2

[47] B. Kaltenbacher, I. Lasiecka, and S. Veljović.
Well-posedness and exponential decay for the Westervelt equation with inhomogeneous Dirichlet boundary data,
In J. Escher et al (Eds): Parabolic Problems: Herbert Amann Festschrift, pages 357-387.
Birkhaeuser, Basel, 2011. Progress in Nonlinear Differential Equations and Their Applications, Vol. 60.

[48] B. Kaltenbacher and J. Offtermatt.
A Refinement and Coarsening Indicator Algorithm for Finding Sparse Solutions of Inverse Problems,
Inverse problems and Imaging (IPI) 5 (2011), pp. 391-406.

[49] B. Kaltenbacher and H. Walk.
On Convergence of Local Averaging Regression Function Estimates for the Regularization of Inverse Problems,
Inverse problems 27 (2011), 035007 doi: 10.1088/0266-5611/27/3/035007

[50] B. Kaltenbacher, I. Lasiecka.
An analysis of nonhomogeneous Kuznetsov's equation: Local and global well-posedness; exponential decay.
Mathematische Nachrichten, 285(2-3):295-321, 2012. DOI 10.1002/mana.201000007.

[51] B. Kaltenbacher, I. Lasiecka.
Well-posedness of the Westervelt and the Kuznetsov equation with nonhomogeneous Neumann boundary conditions, 
DCDS Supplement, Proceedings of the 8th AIMS Conference, 763-773, 2011.

[52] B. Kaltenbacher and J. Offtermatt.
A convergence analysis of regularization by discretization in preimage space.
Mathematics of Computation. 81 (2012) 2049-2069.

[53] B. Kaltenbacher and W. Polifke.
Some regularization methods for a thermoacoustic inverse problem
Journal of Inverse and Ill-Posed Problems (special issue M.V.Klibanov), 18 (2011), pp.997-1011.

[54] B. Kaltenbacher, A. Kirchner, and B. Vexler.
Adaptive discretizations for the choice of a Tikhonov regularization parameter in nonlinear inverse problems.
Inverse Problems, 27:125008, 2011.

[55] B. Kaltenbacher, I. Lasiecka, and R. Marchand.
Wellposedness and exponential decay rates for the Moore-Gibson-Thompson equations arising in high intensity ultrasound.
Control and Cybernetics 40 (2012), pp. 971-989. (invited volume).

[56] B. Kaltenbacher, I. Lasiecka, and M. Pospieszalska.
Wellposedness and exponential decay of the energy in the nonlinear Moore-Gibson-Thompson equation arising in high intensity ultrasound.
M3AS, 22 (2012) 1250035

[57]B. Kaltenbacher.
Convergence rates for the iteratively regularized Landweber iteration in Banach space.
In Proceedings of the 25th IFIP TC7 Conference on System Modeling and Optimization, D. Hömber and F.Tröltzsch, eds., Springer, Berlin, New York, 2012. refereed.

[58] B. Kaltenbacher, M. Kaltenbacher, and I. Sim.
Perfectly matched layer technique for the second order wave equation in time domain.
Journal of Computational Physics 235:407-422, 2013.

[59] C. Clason and B. Kaltenbacher.
On the use of state constraints in optimal control of singular PDEs.
System & Control Letters 62:48-54, 2013.

[60] C. Clason and B. Kaltenbacher.
Avoiding degeneracy in the Westervelt equation by state constrained optimal control.
Evolution Equations and Control Theory (EECT) 2:281-300, 2013.

[61] B. Kaltenbacher and I. Tomba.
Convergence rates for an iteratively regularized Newton-Landweber iteration in Banach space.
Inverse Problems, 29 025010 doi:10.1088/0266-5611/29/2/025010 2013.

[62] C. Clason and B. Kaltenbacher.
Optimal control of a singular PDE modeling transient MEMS with control or state constraints,
Journal of Mathematical Analysis and Applications 410:455-468, 2014.

[63] B. Kaltenbacher, A. Kirchner, and B. Veljović.
Goal-oriented adaptvity in the IRGNM for parameter identification in PDEs I: reduced formulation
Inverse Problems 30 (2014) 045001

[64] B. Kaltenbacher, A. Kirchner, and B. Vexler.
Goal-oriented adaptvity in the IRGNM for parameter identification in PDEs II: all-at-once formulations
Inverse Problems 30 (2014) 045002
  • Adaptive discretization of inverse problems, Inverse Problems Insights article


    • [65] R. Brunnhuber, B.Kaltenbacher and P. Radu.
    Relaxation of regularity for the Westervelt equation by nonlinear damping with application in acoustic-acoustic and elastic-acoustic coupling,
    Evolution Equations and Control Theory EECT, 3 (2014), 595-626.

    [66] R. Brunnhuber and B.Kaltenbacher.
    Well-posedness and asymptotic behavior of solutions for the Blackstock-Crighton rotational model equation,
    Discrete and Continuous Dynamical System - A DCDS-A 34 (2014), 4515-4535.

    [67] B.Kaltenbacher, V. Nikolić and M. Thalhammer
    Efficient time integration methods based on operator splitting and application to the Westervelt equation,
    IMA Journal of Numerical Analysis (2014), doi:10.1093/imanum/dru029, 33 pages.

    [68] B. Kaltenbacher
    A convergence rates result for an iteratively regularized Gauss-Newton-Halley method in Banach space,
    Inverse Problems 31 (2015) 015007.

    [69] B. Kaltenbacher
    An iteratively regularized Gauss-Newton-Halley method for solving nonlinear illposed problems.
    Numerische Mathematik 131(2015) 33-57.

    [70] B. Kaltenbacher and I.Tomba
    Enhanced choice of the parameters in an iteratively regularized Newton-Landweber iteration in Banach space.
    In Dynamical Systems, Differential Equations and Applications; AIMS Proceedings, pages 686-695, 2015. refereed, (AIMS Conference 2014, Madrid).

    [71] I. Shevchenko and B. Kaltenbacher.
    Absorbing boundary conditions for the Westervelt equation.
    In Dynamical Systems, Differential Equations and Applications; AIMS Proceedings, p. 1000-1008, 2015. refereed, (AIMS Conference 2014, Madrid).

    [72] I. Shevchenko and B. Kaltenbacher.
    Absorbing boundary conditions for nonlinear acoustics: The Westervelt equation.
    Journal of Computational Physics 302(2015) 200-221.

    [73] V. Nikolić and B. Kaltenbacher.
    On higher regularity for the Westervelt equation with strong nonlinear damping.
    Applicable Analysis, (2015) 1-17.

    [74] B. Kaltenbacher.
    Mathematics of Nonlinear Acoustics.
    Evolution Equations and Control Theory(EECT), 4(2015) 447-491.

    [75] B. Kaltenbacher and P. Krejčí.
    A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis.
    ZAMM - Journal of Applied Mathematics and Mechanics, published online Dec 2015, doi:10.1002/zamm.201400292

    [76] U. Hämarik, B. Kaltenbacher, U. Kangro, and E. Resmerita.
    Regularization by discretization in Banach spaces
    Inverse Problems 32 (2016) 035004, doi:10.1088/0266-5611/32/3/035004

    [77] R. Boiger and B. Kaltenbacher.
    An online parameter identification method for time dependent partial differential equations.
    Inverse Problems 32 (2016) 045006, doi:10.1088/0266-5611/32/4/045006.

    [78] V. Nikolić and B. Kaltenbacher.
    Sensitivity analysis for shape optimization of a focusing acoustic lens in lithotripsy.
    Applied Mathematics and Optimization, published online March 2016, doi:10.1007/s00245-016-9340-x

    [79] B. Kaltenbacher, E. Resmerita, and F. Rendl.
    Computing quasisolutions of nonlinear inverse problems via efficient minimization of trust region problems.
    Journal of Inverse and Ill-Posed Problems, published online March 2016, doi:10.1515/jiip-2015-00872016.

    [80] B. Kaltenbacher and Gunther Peichl
    The shape derivative for an optimization problem in lithotripsy.
    Evolution Equations and Control Theory(EECT) 5(2016), 399-430.

    [81] B. Hofmann, B. Kaltenbacher, and E. Resmerita.
    Lavrentiev's regularization method in Hilbert spaces revisited.
    Inverse Problems and Imaging 10 (2016), 741-764.

    [82] C. Clason, B. Kaltenbacher, and D. Wachsmuth.
    Functional error estimators for the adaptive discretization of inverse problems.
    Inverse Problems 32 (2016), 104004.

    [83] K. Bredies, B. Kaltenbacher, and E. Resmerita.
    The least error method for sparse solution reconstruction.
    Inverse Problems 32 (2016), 094001.

    [84] B. Kaltenbacher.
    Regularization based on all-at-once formulations for inverse problems.
    SIAM Journal of Numerical Analysis, 54 (2016), 2594-2618.

    [85] B. Kaltenbacher.
    Well-posedness of a general higher order model in nonlinear acoustics
    Applied Mathematics Letters 63 (2016), 21-27.

    [86] R. Boiger, J. Hasenauer, S. Hroß, and B. Kaltenbacher.
    Integration based profile likelihood calculation for PDE constrained parameter estimation problems.
    Inverse Problems 32 (2016), 125009.

    [87] F. Fröhlich, B. Kaltenbacher, F. Theis, and J. Hasenauer.
    Scalable parameter estimation for genome-scale biochemical reaction networks.
    PLOS Computational Biology 13, e1005331, 2017.

    [88] M. Hinze, B.Kaltenbacher, and T.N.T. Quyen.
    Identifying conductivity in electrical impedance tomography with total variation regularization
    Numerische Mathematik, 138(3), 723-765, 2017

    [89] B. Kaltenbacher.
    All-at-once versus reduced iterative methods for time dependent inverse problems
    Inverse Problems 33 064002, 2017

    [90] B. Kaltenbacher.
    Minimization based formulations of inverse problems and their regularization
    SIAM Journal on Optimization 28(1), 620-645, 2018

    [91] B. Kaltenbacher and A. Klassen.
    On convergence and convergence rates for Ivanov and Morozov regularization and application to some parameter identification problems in elliptic PDEs
    Inverse Problems 34 055008, 2018

    [92] B. Kaltenbacher and M.L. Previatti de Souza.
    Convergence and adaptive discretization of the IRGNM Tikhonov and the IRGNM Ivanov method under a tangential cone condition in Banach space
    Numerische Mathematik 140 (2018), 449-478.

    [93] R. Boiger, A. Fiedler, J. Hasenauer, and B. Kaltenbacher. Continuous analogue to iterative optimisation for PDE-constrained inverse problem
    Inverse Problems in Science & Engineering 2018, published online: Jul 2018, doi:10.1080/17415977.2018.1494167

    [94] B. Kaltenbacher and Mechthild Thalhammer.
    Fundamental Models in Nonlinear Acoustics - Part I. Analytical Comparison
    Mathematical Models and Methods in the Applied Sciences M3AS, 28 (2018), 2403-2455.

    [95] B. Kaltenbacher and B. Pedretscher.
    Parameter estimation in SDEs via the Fokker-Planck equation: Likelihood function and adjoint based gradient computation
    Journal of Mathematical Analysis and Applications 465 (2018), 872-884.

    [96] B. Kaltenbacher, M. Kaltenbacher, and S. Gombots.
    Inverse Scheme for Acoustic Source Localization using Microphone Measurements and Finite Element Simulations
    Acta Acustica united with Acustica 104 (2018), 647-656.

    [97] C. Clason, B. Kaltenbacher, and E. Resmerita.
    Regularization of ill-posed problems with non-negative solutions,
    Splitting Algorithms, Modern Operator Theory, and Applications, H. Bauschke, R. Burachik, R. Luke (eds.), Springer, to appear;

    [98] B. Kaltenbacher and P. Krejčí.
    Analysis of an optimization problem for a piezoelectric energy harvester.
    Archive of Applied Mechanics, published online Sep 2018, doi:10.1007/s00419-018-1459-6

    [99] B. Kaltenbacher, A. Klassen and M.L. Previatti de Souza.
    The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius
    Journal of Inverse and Ill-posed Problems, 27:539-557, 2019.

    [100] B. Kaltenbacher and W. Rundell.
    Regularization of a backwards parabolic equation by fractional operators.
    Inverse Problems and Imaging 13 (2019), 401-430.

    [101] B. Kaltenbacher and W. Rundell.
    On an inverse potential problem for a fractional reaction-diffusion equation.
    Inverse Problems, 35:065004, 2019.

    [102] B. Kaltenbacher and W. Rundell.
    On the identification of a nonlinear term in a reaction-diffusion equation.
    Inverse Problems, 35:115007, 2019.

    [103] B. Kaltenbacher and W. Rundell.
    Recovery of multiple coefficients in a reaction-diffusion equation.
    Journal of Mathematical Analysis and Applications, 481:123475, 2019.

    [104] B. Kaltenbacher and I. Shevchenko.
    Well-posedness of the Westervelt equation with higher order absorbing boundary conditions.
    Journal of Mathematical Analysis and Applications, 479:1595-1617, 2019.

    [105] B. Kaltenbacher and V. Nikolić.
    On the Jordan-Moore-Gibson-Thompson equation: well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time.
    Math. Meth. Mod. Appl. Sci. (M3AS), 29:2523-2556, 2019.

    [106] B. Pedretscher, B. Kaltenbacher, and O. Pfeiler.
    Parameter identification and uncertainty quantification in stochastic state space models and its application to texture analysis.
    Applied Numerical Mathematics, 146:38 -- 54, 2019. ISSN 0168-9274. URL http://www.sciencedirect. com/science/article/pii/S0168927419301722.

    [107] B. Kaltenbacher and V. Nikolić.
    Vanishing relaxation time limit of the Jordan-Moore-Gibson-Thompson wave equation with Neumann and absorbing boundary conditions.
    Pure and Applied Functional Analysis, 2019. to appear; special issue dedicated to Irena Lasiecka.

    [108] Philipp Hungerlander, Barbara Kaltenbacher, and Franz Rendl.
    Regularization of inverse problems via box constrained minimization.
    Inverse Problems and Imaging, 14:437-461, 2020.

    [109] Barbara Kaltenbacher.
    Periodic solutions and multiharmonic expansions for the Westervelt equation.
    Evolution Equations and Control Theory EECT, 2020. doi: 10.3934/eect.2020063

    [110] Barbara Kaltenbacher and William Rundell.
    The inverse problem of reconstructing reaction-diffusion systems.
    Inverse Problems 36:065011, 2020.
    and arXiv:2003.00489 [math.NA]

    [111] Barbara Kaltenbacher and William Rundell.
    On the simultaneous recovery of the conductivity and the nonlinear reaction term in a parabolic equation
    Inverse Problems and Imaging, 14:939-966, 2020.

    [112] Kha Van Huynh and B. Kaltenbacher.
    Some application examples of minimization based formulations of inverse problems and their regularization.
    Inverse Problems and Imaging, 15:415-443, 2021. to appear.

    [113] Barbara Kaltenbacher, Tram Thi Ngoc Nguyen, Anne Wald, and Thomas Schuster,
    Parameter identification for the Landau-Lifshitz-Gilbert equation in magnetic particle imaging.
    In Barbara Kaltenbacher, Anne Wald, and Thomas Schuster, editors, Time-dependent Problems in Imaging and Parameter Identification. Springer, New York, 2021.
    and arXiv:1908.01239.

    [114] Barbara Kaltenbacher, Tram Thi Ngoc Nguyen, Anne Wald, and Thomas Schuster,
    Parameter identification for the Landau-Lifshitz-Gilbert equation in magnetic particle imaging.
    In Barbara Kaltenbacher, Anne Wald, and Thomas Schuster, editors, Time-dependent Problems in Imaging and Parameter Identification. Springer, New York, 2021.

    [115] Masahiro Yamamoto and Barbara Kaltenbacher.
    An inverse source problem related to acoustic nonlinearity parameter imaging.
    In Barbara Kaltenbacher, Anne Wald, and Thomas Schuster, editors, Time-dependent Problems in Imaging and Parameter Identification. Springer, New York, 2021.

    [116] Anna Schlintl and Barbara Kaltenbacher.
    All-at-once formulation meets the Bayesian approach: A study of two prototypical linear inverse problems.
    In B. Jadamba, A. Khan, M. Sama, and S. Migorski, editors, Deterministic and Stochastic Optimal Control and Inverse Problems, CRC Press, 2021.

    [117] Barbara Kaltenbacher and Mechthild Thahammer.
    Convergence of implicit Runge-Kutta time discretisation methods for fundamental models in nonlinear acoustics.
    Journal of Applied and Numerical Optimization, 3:361–401, 2021. special issue dedicated to Joachim Gwinner.

    [118] Barbara Kaltenbacher and William Rundell.
    Some inverse problems for wave equations with fractional derivative attenuation.
    Inverse Problems, 37(4):045002, mar 2021. URL https: //doi.org/10.1088/1361-6420/abe136.

    [119] Barbara Kaltenbacher and William Rundell.
    On the identification of the nonlinearity parameter in the westervelt equation from boundary measurements.
    Inverse Problems & Imaging, 15:865-891, 2021. ISSN 1930-8337. URL http://aimsciences.org//article/id/ 614ee729-b72d-424c-a1bf-cc0b322fd9f6.

    [120] Barbara Kaltenbacher and William Rundell.
    On uniqueness and reconstruction of a nonlinear diffusion term in a parabolic equation.
    Journal of Mathematical Analysis and Applications, 500: 125145, 2021. see also arXiv:2101.06696 [math.AP].

    [121] Barbara Kaltenbacher and Vanja Nikolić.
    The inviscid limit of third-order linear and nonlinear acoustic equations.
    SIAM Journal on Applied Mathematics, 81:1461-1482, 2021. see also arXiv:2101.05488 [math.AP].

    [122] Barbara Kaltenbacher and Tram Thi Ngoc Nguyen.
    A model reference adaptive system approach for nonlinear online parameter identification.
    Inverse Problems, 37:055006, 2021. URL https://iopscience.iop.org/article/10.1088/1361-6420/abf164. see also arXiv:2012.09908 [math.OC].

    [123] Barbara Kaltenbacher and Kha Van Huynh.
    Iterative regularization for constrained minimization formulations of nonlinear inverse problems.
    Computational Optimization and Applications, 81:569-611, 2021. URL https://doi.org/10.1007/s10589-021-00343-x. see also arXiv:2101.05482 [math.NA].

    [124] Barbara Kaltenbacher and William Rundell.
    On an inverse problem of nonlinear imaging with fractional damping.
    Mathematics of Computation, 91:245-276, 2022. see also arXiv:2103.08965 [math.AP].

    [125] Barbara Kaltenbacher and Anna Schlintl.
    Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation.
    Journal of Computational Physics, 449:110789, 2022. see also arXiv:2104.05577 [math.NA].

    [126] Stefan Gombots, Manfred Kaltenbacher, and Barbara Kaltenbacher.
    Capabilities of inverse scheme for acoustic source localization at low frequencies.
    Acta Acustica, 5:647-656, 2021.

    [127] Barbara Kaltenbacher and William Rundell.
    Determining the nonlinearity in an acoustic wave equation.
    Mathematical Methods in the Applied Sciences M2AS, 45:3554-3573, 2021. see also arXiv:2107.04058 [math.NA].

    [128] Barbara Kaltenbacher and Vanja Nikolić.
    Parabolic approximation of quasilinear wave equations with applications in nonlinear acoustics.
    SIAM Journal on Mathematical Analysis, 54:1593–1622, 2022. see also arXiv:2011.07360.

    [129] Barbara Kaltenbacher.
    On the inverse problem of vibro-acoustography.
    Meccanica, 2022; see also arXiv:2109.01907 [math.AP].

    [130] Barbara Kaltenbacher and Vanja Nikolić.
    Time-fractional Moore-Gibson-Thompson equations.
    Mathematical Models and Methods in the Applied Sciences M3AS, 32:965–1013, 2022. see also arXiv:2104.13967 [math.AP].

    [131] Barbara Kaltenbacher and William Rundell.
    Determining damping terms in fractional wave equations. Inverse Problems 38:075004, 2022. see also arXiv:2109.01907 [math.AP].

    [132] Barbara Kaltenbacher, Ustim Khristenko, Vanja Nikolić, Mabel Lizzy Rajendran, and Barbara Wohlmuth.
    Determining kernels in linear viscoelasticity. Journal of Computational Physics 464:111331, 2022. see also arXiv:2112.14071 [math.AP].

    [133] Barbara Kaltenbacher and Tram Thi Ngoc Nguyen.
    Discretization of parameter identication in PDEs using Neural Networks. Inverse Problems, 38:124007, 2022. see also arXiv:2012.09908 [math.OC].

    [134] Barbara Kaltenbacher and William Rundell.
    On the determination of a coefficient in a space- fractional equation with operators of Abel type. Journal of Mathematical Analysis and Applications, 516:126539, 2022.

    [135] Barbara Kaltenbacher.
    Convergence guarantees for coefficient reconstruction in PDEs from boundary measurements by variational and Newton-type methods via range invariance. IMA Journal of Numerical Analysis, page drad044, 07 2023. ISSN 0272-4979. URL https://doi.org/10.1093/ imanum/drad044. see also arXiv:2209.12596 [math.NA].

    [136] Barbara Kaltenbacher and William Rundell.
    Nonlinearity parameter imaging in the frequency domain. Inverse Problems and Imaging, 2023. see also arXiv:2303.09796 [math.NA].

    [137] Barbara Kaltenbacher and William Rundell.
    On the simultanenous reconstruction of two space dependent coefficients in acoustic nonlinearity parameter tomography. Inverse Problems, 39: 105001, 2023. see also arXiv:2210.08063 [math.NA].

    [138] Barbara Kaltenbacher and Vanja Nikolić.
    The vanishing relaxation time behavior of multi-term nonlocal Jordan-Moore-Gibson-Thompson equations. Nonlinear Analysis: Real World Applications, 2023. to appear; see also arXiv:2302.06196 [math.AP].

    [139] Barbara Kaltenbacher.
    Identifiability of some space dependent coefficients in a wave equation of nonlinear acoustics. Evolution Equations and Control Theory, 2023. to appear; see also arXiv:2305.04110 [math.AP].

    [140] Barbara Kaltenbacher and Teresa Rauscher.
    Simultaneous reconstruction of sound speed and nonlinearity parameter in a paraxial model of vibro-acoustography in frequency domain. 2023. submitted; see also arXiv:2303.17236 [math.NA].

    [141] Barbara Kaltenbacher and Amjad Tuffaha.
    Well-posedness of a nonlinear acoustics - structure interaction model. 2023. submitted; see also arXiv:2308.11274 [math.AN].

    [142] Barbara Kaltenbacher, Mostafa Meliani, and Vanja Nikolić.
    Limiting behavior of quasilinear wave equations with fractional-type dissipation. 2023. submitted; see also arXiv:2206.15245 [math.AP].

    [143] Barbara Kaltenbacher, Mostafa Meliani, and Vanja Nikolić.
    The Kuznetsov and Blackstock equations of nonlinear acoustics with nonlocal-in-time dissipation. 2023. submitted; see also arXiv:2206.15245 [math.AP].

    [144] Barbara Kaltenbacher and William Rundell.
    Regularising the Cauchy problem for Laplace’s equation by fractional operators. 2023. submitted; see also arXiv:2309.13617 [math.NA].


    Proceedings papers

    [1] B. Kaltenbacher, M. Kaltenbacher, R. Lerch, and R. Simkovics
    Identification of material tensors for piezoceramic materials
    In Proceedings of the IEEE Ultrasonics Symposium, volume 2, pages 1033-1036. IEEE, 2000

    [2] M. Kaltenbacher, B. Kaltenbacher, R. Simkovics, and R. Lerch
    Determination of piezoelectric material parameters using a combined measurement and simulation technique
    In Proceedings of the IEEE Ultrasonics Symposium, pages 1023-1026. IEEE, 2001

    [3] B. Kaltenbacher, M. Kaltenbacher, R. Lerch, R. Simkovics, and S. Reitzinger
    Determination of Material Parameters Based on Field Computations and Regularized Iterative Inversion
    In Proceedings of MATHMOD. MATHMOD, 2003. (Wien)

    [4] B. Kaltenbacher, M. Hofer, M. Kaltenbacher, and R. Lerch
    Identification of material nonlinearities in piezoelectric ceramics
    In Proceedings of the IEEE Ultrasonics Symposium. IEEE, 2003. (Honolulu, 05.-08.10.2003)

    [5] B. Kaltenbacher, M. Hofer, M. Kaltenbacher, and R. Lerch
    Piezoelectric material nonlinearity identification via multiharmonic finite elements
    In Proceedings of the IEEE Ultrasonics Symposium, 2004

    [6] B. Kaltenbacher
    Identification of models for nonlinearity and hysteresis in piezoelectricity
    In D.R.J. Owen, E. Onate, and B. Suarez, eds., Computational Plasticity/ COMPLAS VIII, pages 657-660. CIMNE, 2005. (Barcelona)

    [7] S. Gombots, M. Kaltenbacher, and B. Kaltenbacher.
    Inverse scheme for acoustic source localization in 3D,
    EURONOISE 2018.