33 citations · 303 across the 46 of their papers we have counts for
57 papers
Regularising the Cauchy problem for Laplace's equation by fractional operators
Barbara Kaltenbacher an William Rundell
In this paper we revisit the classical Cauchy problem for Laplace's equation as well as two further related problems in the light of regularisation of this highly ill-conditioned p…
Well-posedness of a Nonlinear Acoustics -- Structure Interaction Model
Barbara Kaltenbacher, Amjad Tuffaha
We establish local-in-time and global in time well-posedness for small data, for a coupled system of nonlinear acoustic structure interactions. The model consists of the nonlinear…
Uniqueness of some space dependent coefficients in a wave equation of nonlinear acoustics
Barbara Kaltenbacher
In this paper we prove uniqueness for some parameter identification problems for the JMGT equation, a third order in time quasilinear PDE in nonlinear acoustics. The coefficients t…
Simultaneous reconstruction of sound speed and nonlinearity parameter in a paraxial model of vibro-acoustography in frequency domain
Barbara Kaltenbacher ans teresa Rauscher
In this paper we consider the inverse problem of vibro-acoustography, a technique for enhancing ultrasound imaging by making use of nonlinear effects. It amounts to determining two…
Nonlinearity parameter imaging in the frequency domain
Barbara Kaltenbacher, William Rundell
Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation.…
The vanishing relaxation time behavior of multi-term nonlocal Jordan-Moore-Gibson-Thompson equations
Barbara Kaltenbacher, Vanja Nikolić
The family of Jordan-Moore-Gibson-Thompson (JMGT) equations arises in nonlinear acoustics when a relaxed version of the heat flux law is employed within the system of governing equ…
On the simultanenous identification of the nonlinearity coefficient and the sound speed in the Westervelt equation
Barbara Kaltenbacher, William Rundell
This paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importa…
Convergence guarantees for coefficient reconstruction in PDEs from boundary measurements by variational and Newton type methods via range invariance
Barbara Kaltenbacher
A key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear ill-posed operator equations -- such…
Limiting behavior of quasilinear wave equations with fractional-type dissipation
Barbara Kaltenbacher, Mostafa Meliani, Vanja Nikolić
In this work, we investigate a class of quasilinear wave equations of Westervelt type with, in general, nonlocal-in-time dissipation. They arise as models of nonlinear sound propag…
Determining kernels in linear viscoelasticity
Barbara Kaltenbacher, Ustim Khristenko, Vanja Nikolić +2
In this work, we investigate the inverse problem of determining the kernel functions that best describe the mechanical behavior of a complex medium modeled by a general nonlocal vi…
Determining damping terms in fractional wave equations
Barbara Kaltenbacher, William Rundell
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstr…
On the inverse problem of vibro-acoustography
Barbara Kaltenbacher
The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and re…
Discretization of parameter identification in PDEs using Neural Networks
Barbara Kaltenbacher, Tram Thi Ngoc Nguyen
We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determi…
Determining the nonlinearity in an acoustic wave equation
Barbara Kaltenbacher, William Rundell
We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical ima…
Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation
Barbara Kaltenbacher, Anna Schlintl
In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photo…
Time-fractional Moore-Gibson-Thompson equations
Barbara Kaltenbacher, Vanja Nikolić
In this paper, we consider several time-fractional generalizations of the Jordan-Moore-Gibson-Thompson (JMGT) equations in nonlinear acoustics as well as their linear Moore-Gibson-…
On an inverse problem of nonlinear imaging with fractional damping
Barbara Kaltenbacher, William Rundell
This paper considers the attenuated Westervelt equation in pressure formulation. The attenuation is by various models proposed in the literature and characterised by the inclusion…
On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements
Barbara Kaltenbacher, William Rundell
We consider an undetermined coefficient inverse problem for a non-\\linear partial differential equation occurring in high intensity ultrasound propagation as used in acoustic tomo…
On uniqueness and reconstruction of a nonlinear diffusion term in a parabolic equation
Barbara Kaltenbacher, William Rundell
The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time sca…
On the simultaneous recovery of the conductivity and the nonlinear reaction term in a parabolic equation
Barbara Kaltenbacher, William Rundell
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity and the nonlinear reaction term in a reaction-diffusion equa…
All-at-once formulation meets the Bayesian approach: A study of two prototypical linear inverse problems
Anna Schlintl, Barbara Kaltenbacher
In this work, the Bayesian approach to inverse problems is formulated in an all-at-once setting. The advantages of the all-at-once formulation are known to include the avoidance of…
Iterative regularization for constrained minimization formulations of nonlinear inverse problems
Barbara Kaltenbacher, Kha Van Huynh
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analys…
The inviscid limit of third-order linear and nonlinear acoustic equations
Barbara Kaltenbacher, Vanja Nikolić
We analyze the behavior of third-order in time linear and nonlinear sound waves in thermally relaxing fluids and gases as the sound diffusivity vanishes. The nonlinear acoustic pro…
A model reference adaptive system approach for nonlinear online parameter identification
Barbara Kaltenbacher, Tram Thi Ngoc Nguyen
Dynamical systems, for instance in model predictive control, often contain unknown parameters, which must be determined during system operation. Online or on-the-fly parameter iden…