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This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…

Analysis of PDEs · Mathematics 2024-03-14 Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang

This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…

Analysis of PDEs · Mathematics 2018-04-26 Cătălin I. Cârstea

Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…

Analysis of PDEs · Mathematics 2026-04-13 Rima Alaifari , Giovanni S. Alberti , Tandri Gauksson

Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…

Analysis of PDEs · Mathematics 2019-09-09 Shahah Almutairi , Ajith Gunaratne

In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…

Analysis of PDEs · Mathematics 2025-03-07 Pu-Zhao Kow , Mikko Salo , Sen Zou

In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz…

Analysis of PDEs · Mathematics 2021-11-08 Rogelio Arancibia , Rodrigo Lecaros , Alberto Mercado , Sebastián Zamorano

We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…

Analysis of PDEs · Mathematics 2024-05-27 Lauri Oksanen , Tianyu Yang , Yang Yang

In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…

Analysis of PDEs · Mathematics 2024-11-08 Suliang Si

We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…

Analysis of PDEs · Mathematics 2026-03-11 Tianyu Yang , Yang Yang

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…

Analysis of PDEs · Mathematics 2024-03-21 Tianjiao Wang , Xiang Xu , Yue Zhao

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…

Analysis of PDEs · Mathematics 2020-05-19 Faouzi Triki , Tao Yin

When a porous rock is saturated with an electrolyte, electrical fields are coupled with seismic waves via the electro-seismic conversion. Pride derived the governing models, in which Maxwell equations are coupled with Biot equations through…

Analysis of PDEs · Mathematics 2015-06-15 Jie Chen , Yang

We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…

Analysis of PDEs · Mathematics 2024-09-10 Giovanni Covi , Jesse Railo , Teemu Tyni , Philipp Zimmermann

This paper concerns an inverse boundary value problem of recovering a zeroth order time-dependent term of a semi-linear wave equation on a globally hyperbolic Lorentzian manifold. We show that an unknown potential $q$ in the non-linear wave…

Analysis of PDEs · Mathematics 2025-05-14 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

Analysis of PDEs · Mathematics 2014-09-29 Lucie Baudouin , Sylvain Ervedoza , Axel Osses

We propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the current can be uniquely reconstructed with Lipschitz stability. We…

Analysis of PDEs · Mathematics 2022-02-25 Wei Li , John C. Schotland , Yang Yang , Yimin Zhong

This paper deals with the reconstruction of small-amplitude perturbations in the electric properties (permittivity and conductivity) of a medium from boundary measurements of the electric field at a fixed frequency. The underlying model is…

Numerical Analysis · Mathematics 2019-11-07 Marion Darbas , Jérémy Heleine , Stephanie Lohrengel

We study the time-harmonic Maxwell equations on bounded Lipschitz domains with an impedance boundary condition. The impedance coefficient can be matrix valued such that, in particular, a polarization dependent impedance is modeled. We…

Analysis of PDEs · Mathematics 2025-10-17 Ben Schweizer , David Wiedemann

This article studies an inverse problem for a transmission wave equation, a system where the main coefficient has a variable jump across an internal interface given by the boundary between two subdomains. The main result obtains Lipschitz…

Analysis of PDEs · Mathematics 2024-09-11 L Baudouin , A Imba , A Mercado , A Osses