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We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information…

Numerical Analysis · Mathematics 2012-10-30 Adriano De Cezaro , B. Tomas Johansson

In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different…

Analysis of PDEs · Mathematics 2022-11-09 Hanin Al Jebawy , Abdellatif El Badia , Faouzi Triki

We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…

Analysis of PDEs · Mathematics 2015-11-05 Maarten V. de Hoop , Lauri Oksanen , Justin Tittelfitz

This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…

Analysis of PDEs · Mathematics 2021-06-16 Yavar Kian

Recently, the Strichartz estimates for the damped wave equation was obtained by the first author except for the wave endpoint case. In the present paper, we give the Strichartz estimate in the wave endpoint case. We slightly modify the…

Analysis of PDEs · Mathematics 2019-07-01 Takahisa Inui , Yuta Wakasugi

We consider the Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence…

Analysis of PDEs · Mathematics 2017-06-14 Ryo Ikehata , Hiroshi Takeda

An inverse problem for the wave equation outside an obstacle with a {\it dissipative boundary condition} is considered. The observed data are given by a single solution of the wave equation generated by an initial data supported on an open…

Analysis of PDEs · Mathematics 2016-07-22 Masaru Ikehata

We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.

Analysis of PDEs · Mathematics 2020-01-24 Rohit Kumar Mishra , Manmohan Vashisth

We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for…

Analysis of PDEs · Mathematics 2025-03-06 Francesco Maddalena , Gianluca Orlando

In this paper we study the uniqueness and the increasing stability in the inverse source problem for electromagnetic waves in homogeneous and inhomogeneous media from boundary data at multiple wave numbers. For the unique determination of…

Analysis of PDEs · Mathematics 2020-07-03 Victor Isakov , Jenn-Nan Wang

This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…

Numerical Analysis · Mathematics 2021-01-14 Xiaoli Feng , Meixia Zhao , Peijun Li , Xu Wang

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…

Analysis of PDEs · Mathematics 2019-04-12 Daijun Jiang , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

In this paper, the simultaneous identification of damping or anti-damping coefficient and initial value for some PDEs is considered. An identification algorithm is proposed based on the fact that the output of system happens to be…

Analysis of PDEs · Mathematics 2016-05-18 Zhi-Xue Zhao , Mapundi Kondwani Banda , Bao-Zhu Guo

This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…

Analysis of PDEs · Mathematics 2025-09-22 Xu Wang , Guanlin Yang , Zhidong 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

We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the…

Analysis of PDEs · Mathematics 2026-03-24 Antonio Arnal , Borbala Gerhat , Julien Royer , Petr Siegl

The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is…

Analysis of PDEs · Mathematics 2014-01-03 Sebastian Acosta , Sum Chow , James Taylor , Vianey Villamizar

We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data…

Analysis of PDEs · Mathematics 2026-01-19 Emilia L. K. Blåsten , Tapio Helin , Antti Kujanpää , Lauri Oksanen , Jesse Railo

In this work, we consider the time-harmonic inverse elastic source problem of a fixed frequency for the Navier equation in two dimensions. We show that a convex polygon can be uniquely determined by a single far field measurement. Our…

Analysis of PDEs · Mathematics 2025-06-04 Jianli Xiang