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We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…

Analysis of PDEs · Mathematics 2021-01-27 Peter Hintz , Gunther Uhlmann , Jian Zhai

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 reconstruction, some of them relying on Tauberian theorems on the…

Analysis of PDEs · Mathematics 2022-06-22 Barbara Kaltenbacher , William Rundell

In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically,…

Analysis of PDEs · Mathematics 2024-10-02 Ru-Yu Lai , Hanming Zhou

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

In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear…

Analysis of PDEs · Mathematics 2026-04-07 Rahul Bhardwaj , Mandeep Kumar , Manmohan Vashisth

We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a…

Analysis of PDEs · Mathematics 2024-05-13 Ru-Yu Lai , Gunther Uhlmann , Hanming Zhou

We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…

Analysis of PDEs · Mathematics 2026-03-30 Sergei Avdonin , Matti Lassas , Jinpeng Lu , Medet Nursultanov , Lauri Oksanen

We study an inverse problem of determining a time-dependent damping coefficient and potential appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of…

Analysis of PDEs · Mathematics 2024-07-26 Boya Liu , Teemu Saksala , Lili Yan

This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…

Analysis of PDEs · Mathematics 2024-02-09 Yi-Hsuan Lin , Teemu Tyni , Philipp Zimmermann

We consider inverse problems for a Westervelt equation with a strong damping and a time-dependent potential $q$. We first prove that all boundary measurements, including the initial data, final data, and the lateral boundary measurements,…

Analysis of PDEs · Mathematics 2023-09-22 Li Li , Yang Zhang

This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…

Analysis of PDEs · Mathematics 2026-05-28 Dong Qiu , Xiang Xu , Yeqiong Ye , Ting Zhou

In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density coefficient…

Analysis of PDEs · Mathematics 2024-04-17 Anamika Purohit

We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms…

Analysis of PDEs · Mathematics 2020-11-13 Yavar Kian , Gunther Uhlmann

We study the unique recovery of time-independent lower order terms appearing in the symmetric first order perturbation of the Riemannian wave equation by sending and measuring waves in disjoint open sets of \textit{a priori} known closed…

Analysis of PDEs · Mathematics 2025-10-30 Matti Lassas , Boya Liu , Teemu Saksala , Andrew Shedlock , Ziyao Zhao

We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known…

Analysis of PDEs · Mathematics 2024-05-03 Rohit Kumar Mishra , Anamika Purohit , Manmohan Vashisth

We study an inverse problem of determining a time-dependent potential appearing in the wave equation in conformally transversally anisotropic manifolds of dimension three or higher. These are compact Riemannian manifolds with boundary that…

Analysis of PDEs · Mathematics 2024-10-22 Boya Liu , Teemu Saksala , Lili Yan

This article develops the numerical and theoretical study of a reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate.…

Numerical Analysis · Mathematics 2016-10-25 Lucie Baudouin , Maya de Buhan , Sylvain Ervedoza

In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is…

Analysis of PDEs · Mathematics 2025-11-20 K. Van Bockstal , K. Khompysh

We deal with two dynamical systems associated with a Riemannian manifold with boundary. The first one is a system governed by the scalar wave equation, the second is governed by the Maxwell equations. Both of the systems are controlled from…

Mathematical Physics · Physics 2015-06-19 M. I. Belishev , M. N. Demchenko

This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic…

Analysis of PDEs · Mathematics 2026-04-15 Irina Kmit , Nataliya Protsakh , Viktor Tkachenko
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