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Related papers: Stability for time-dependent inverse transport

200 papers

In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…

Analysis of PDEs · Mathematics 2016-11-07 Yacine Chitour , Guilherme Mazanti , Mario Sigalotti

This paper is concerned with the inverse acoustic scattering problems of reconstructing time-dependent multiple point sources and sources on a curve $L$ of the form $\lambda(t)\tau(x)\delta_L(x)$. A direct sampling method with a novel…

Numerical Analysis · Mathematics 2023-09-07 Jiaru Wang , Bo Chen , Qingqing Yu , Yao Sun

This paper is concerned with the stability of the inverse boundary value problem for the perturbed fourth-order Schr\"{o}dinger equation in a bounded domain with Cauchy data. We establish stability results for the perturbed potential…

Analysis of PDEs · Mathematics 2025-12-23 Yang Liu , Yixian Gao

We propose a new approach to measuring the agreement between two oscillatory time series, such as seismic waveforms, and demonstrate that it can be employed effectively in inverse problems. Our approach is based on Optimal Transport theory…

Geophysics · Physics 2022-07-01 Malcolm Sambridge , Andrew Jackson , Andrew P. Valentine

This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…

Numerical Analysis · Mathematics 2025-10-28 Xu Wu , Jiang Yang , Zhi Zhou

In this paper, we consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map. To this end, we prove a Lipschitz stability estimate for Lam\'e parameters with certain regularity assumptions. In…

Numerical Analysis · Mathematics 2022-12-13 Sarah Eberle , Bastian Harrach , Houcine Meftahi , Taher Rezgui

We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…

Spectral Theory · Mathematics 2025-08-18 Lung-Hui Chen

We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…

Analysis of PDEs · Mathematics 2024-12-20 Alexander Konschin , Armin Lechleiter

We study the stability in the inverse problem of determining the time dependent zeroth-order coefficient $q(t,x)$ arising in the wave equation, from boundary observations. We derive, in dimension $n\geq 2$, a log-type stability estimate in…

Analysis of PDEs · Mathematics 2015-12-09 Ibtissem Ben Aïcha

In this paper we consider the inverse scattering problem for the Schr{\"o}dinger operator with short-range electric potential. We prove in dimension n $\geq$ 2 that the knowledge of the scattering operator determines the electric potential…

Analysis of PDEs · Mathematics 2018-09-07 Luc Robbiano , Mourad Bellassoued

We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…

Dynamical Systems · Mathematics 2022-04-12 Yunan Yang , Levon Nurbekyan , Elisa Negrini , Robert Martin , Mirjeta Pasha

This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…

Numerical Analysis · Mathematics 2025-09-05 Théophile Chaumont-Frelet , Heiko Gimperlein , Ignacio Labarca-Figueroa , Jörg Nick

In this work, we study the instability of an inverse problem of radiative transport equation with angularly averaged measurement near the diffusion limit, i.e. the normalized mean free path (the Knudsen number) $0 < \eps \ll 1$. It is…

Mathematical Physics · Physics 2022-06-14 Hongkai Zhao , Yimin Zhong

This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…

Analysis of PDEs · Mathematics 2017-09-13 Yue Zhao , Peijun Li

This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…

Analysis of PDEs · Mathematics 2020-07-27 Kaïs Ammari , Boumediène Chentouf , Nejib Smaoui

We give a principled approach for the selection of a boundary integral, retarded potential representation for the solution of scattering problems for the wave equation in an exterior domain.

Numerical Analysis · Mathematics 2015-04-17 Charles L. Epstein , Leslie Greengard , Thomas Hagstrom

We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…

Analysis of PDEs · Mathematics 2016-09-21 Kais Ammari , Mourad Choulli , Faouzi Triki

We show that the inverse problems for a class of kinetic equations can be solved by classical tools in PDE analysis including energy estimates and the celebrated averaging lemma. Using these tools, we give a unified framework for the…

Analysis of PDEs · Mathematics 2020-04-22 Qin Li , Weiran Sun

This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface…

Numerical Analysis · Mathematics 2018-04-09 Guanghui Hu , Xiaoli Liu , Bo Zhang , Haiwen Zhang

This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…

Analysis of PDEs · Mathematics 2024-08-01 Adel Blouza , Léo Glangetas , Yavar Kian , Van-Sang Ngo