English
Related papers

Related papers: On an inverse boundary value problem for a nonline…

200 papers

We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous reference can be uniquely determined by (single-)scattered…

Analysis of PDEs · Mathematics 2026-05-01 Matti Lassas , Shiqi Ma , Lauri Oksanen , Mikko Salo , Jian Zhai

This work considers Bayesian experimental design for the inverse boundary value problem of linear elasticity in a two-dimensional setting. The aim is to optimize the positions of compactly supported pressure activations on the boundary of…

Numerical Analysis · Mathematics 2023-09-06 Sarah Eberle-Blick , Nuutti Hyvönen

The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…

Analysis of PDEs · Mathematics 2023-05-10 Ali Feizmohammadi , Matti Lassas , Lauri Oksanen

In this paper, we consider the inverse boundary problems of recovering the time-dependent nonlinearity and damping term for a semilinear wave equation on a Riemannian manifold. The Carleman estimate and the construction of Gaussian beams…

Analysis of PDEs · Mathematics 2022-12-08 Song-Ren Fu

We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…

Analysis of PDEs · Mathematics 2015-06-11 Mourad Bellassoued , Michel Cristofol , Eric Soccorsi

We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…

Analysis of PDEs · Mathematics 2018-07-11 Monika Pichler

We consider an inverse problem of recovering a parameter appearing in all levels in a second-order hyperbolic equation from a single boundary measurement. The model is motivated from applications in photoacoustic tomography when one seeks…

Analysis of PDEs · Mathematics 2024-08-26 Shitao Liu , Gunther Uhlmann , Yang Yang

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

Analysis of PDEs · Mathematics 2014-12-12 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella , Jian Zhai

In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric…

Numerical Analysis · Mathematics 2024-10-04 Jérémy Heleine

We consider inverse boundary value problems for the Jordan-Moore-Gibson-Thompson (JMGT) equation in nonlinear acoustics with quadratic nonlinearities of Kuznetsov-type and Westervelt-type. We show that the associated boundary…

Analysis of PDEs · Mathematics 2026-04-10 Dong Qiu , Xiang Xu , Yeqiong Ye , Ting Zhou

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) resistors. Generalizing work of Curtis, Ingerman, Morrow, Colin de Verdiere, Gitler, and Vertigan, we characterize…

Combinatorics · Mathematics 2012-03-20 Will Johnson

We consider the inverse boundary value problem of recovering piecewise homogeneous elastic tensor and piecewise homogeneous mass density from a localized lateral Dirichlet-to-Neumann or Neumann-to-Dirichlet map for the elasticity equation…

Analysis of PDEs · Mathematics 2019-03-05 Cătălin I. Cârstea , Gen Nakamura , Lauri Oksanen

In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material parameters and the nonlinear susceptibility parameters of…

Analysis of PDEs · Mathematics 2020-09-15 Yernat M. Assylbekov , Ting Zhou

We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\Omega$ in $\R^n, n\geq 2$. We recover the coefficients at the boundary from the…

Analysis of PDEs · Mathematics 2024-01-12 Nitesh Kumar , Tanmay Sarkar , Manmohan Vashisth

In this paper we prove uniqueness in the inverse boundary value problem for quasilinear elliptic equations whose linear part is the Laplacian and nonlinear part is the divergence of a function analytic in the gradient of the solution. The…

Analysis of PDEs · Mathematics 2023-05-10 Cătălin I. Cârstea , Ali Feizmohammadi

We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear…

Analysis of PDEs · Mathematics 2011-06-22 Mikko Salo , Xiao Zhong

We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…

Analysis of PDEs · Mathematics 2025-09-24 A. S. Mikhaylov , V. S. Mikhaylov

In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured…

Analysis of PDEs · Mathematics 2015-02-06 Francis J. Chung , Petri Ola , Mikko Salo , Leo Tzou

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.

Analysis of PDEs · Mathematics 2019-06-24 Manmohan Vashisth

We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity…

Analysis of PDEs · Mathematics 2025-03-27 R. M. Brown , L. D. Gauthier