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This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…

Analysis of PDEs · Mathematics 2025-04-25 Qi Lü , Yu Wang

We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A…

Numerical Analysis · Mathematics 2019-12-16 Khaled M. Furati , Kassem Mustapha , Ibrahim O. Sarumi , Olaniyi S. Iyiola

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain…

Analysis of PDEs · Mathematics 2018-04-04 Gang Bao , Guanghui Hu , Yavar Kian , Tao Yin

In the present work, we discuss a unique solvability of an inverse-source problem with integral transmitting condition for time-fractional mixed type equation in a rectangular domain, where the unknown source term depends on space variable…

Analysis of PDEs · Mathematics 2016-04-01 Erkinjon Karimov , Nasser Al-Salti , Sebti Kerbal

This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…

Optimization and Control · Mathematics 2013-10-01 Zui-Cha Deng , Liu Yang

We examine various density results related to the solutions of the non-local heat equation at a specific time slice, focusing on two distinct models: one with homogeneous Dirichlet boundary condition and the other with singular boundary…

Analysis of PDEs · Mathematics 2025-12-30 Saumyajit Das

We consider two phaseless inverse problems for elliptic equation. The statements of these problems differ from have considered. Namely, instead of given information about modulus of scattering waves, we consider the information related to…

Analysis of PDEs · Mathematics 2018-01-31 V. G. Romanov , M. Yamamoto

In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…

Numerical Analysis · Mathematics 2025-08-22 Tianhao Hu , Xinchi Huang , Bangti Jin , Qimeng Quan , Zhi Zhou

This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order $\alpha\in(0,2]$ in time. In the first problem, the sources are supposed to move along known…

Analysis of PDEs · Mathematics 2023-01-03 Yikan Liu , Guanghui Hu , Masahiro Yamamoto

In this paper, we study the flux identification problem for a nonlinear time-fractional viscoelastic equation with a general source function based on the boundary measurements. We prove that the direct problem is well-posed, i.e., the…

Analysis of PDEs · Mathematics 2024-07-24 Mohamed BenSalah , Salih Tatar , Suleyman Ulusoy , Masahiro Yamamoto

In this work the authors consider the recovery of the point source in the heat equation. The used data is the sparse boundary measurements. The uniqueness theorem of the inverse problem is given. After that, the numerical reconstruction is…

Numerical Analysis · Mathematics 2025-02-06 Qiling Gu , Wenlong Zhang , Zhidong Zhang

The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the…

Numerical Analysis · Mathematics 2020-04-16 Alexey Smirnov , Michael Klibanov , Anders Sullivan , Lam Nguyen

In this paper we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the…

Statistics Theory · Mathematics 2023-11-30 Aksel Kaastrup Rasmussen , Fanny Seizilles , Mark Girolami , Ieva Kazlauskaite

In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…

Analysis of PDEs · Mathematics 2013-07-30 Manabu Machida , Masahiro Yamamoto

Inverse problem for multi-term fractional parabolic equation in two dimensional space, involving m + 1 Caputo fractional derivatives in time, is investigated. Presence of nonlocal boundary conditions leads to a non-self-adjoint spectral…

Analysis of PDEs · Mathematics 2022-02-08 Muhammad Ali , Sara Aziz

We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on…

Analysis of PDEs · Mathematics 2022-10-11 Shitao Liu , Antonio Pierrottet , Scott Scruggs

In this article, for an advection-diffusion equation we study an inverse problem for restoration of source temperature from the information of final temperature profile. The uniqueness of this inverse problem is established by taking an…

Analysis of PDEs · Mathematics 2018-06-15 Zhiyuan Li , Gongsheng Li , Xianzheng Jia

In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order $\alpha\in(0,1)$ in time, from the terminal data. We prove that the inverse…

Numerical Analysis · Mathematics 2020-09-09 Bangti Jin , Zhi Zhou

Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models,…

Chaotic Dynamics · Physics 2015-05-18 Hadrien Bosetti , Harald A. Posch , Christoph Dellago , William G. Hoover

We consider inverse problems for wave, heat and Schr\"odinger-type operators and corresponding spectral problems on domains of ${\bf R}^n$ and compact manifolds. Also, we study inverse problems where coefficients of partial differential…

Analysis of PDEs · Mathematics 2007-05-23 Alexander Katchalov , Yaroslav Kurylev , Matti Lassas , Niculae Mandache