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This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…

Numerical Analysis · Mathematics 2024-04-02 Mengjie Zhao , Suliang Si , Guanghui Hu

In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary…

Mathematical Physics · Physics 2008-05-06 Daveau Christian , Khelifi Abdessatar , Shamma M. Nour

In this paper we investigate direct and inverse problems for time-fractional pseudo-parabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proved. Also, the stability result of the inverse…

Analysis of PDEs · Mathematics 2023-01-03 Bayan Bekbolat , Niyaz Tokmagambetov

In this article, we study an inverse problem consisting in the identification of a space-time dependent source term in the Ginzburg-Landau equation from final-time observations. We adopt a weak-solution framework and analyze Tikhonov's…

Analysis of PDEs · Mathematics 2025-11-11 Roberto Morales , Javier-Ramírez-Ganga

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

A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition at the face $x=0$ is studied with the aim of finding explicit…

Analysis of PDEs · Mathematics 2014-10-16 Andrea N. Ceretani , Domingo A. Tarzia , Luis T. Villa

This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…

Analysis of PDEs · Mathematics 2018-08-13 Zhiyuan Li , Kenichi Fujishiro , Gongsheng Li

This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary)…

Analysis of PDEs · Mathematics 2016-02-10 Aymen Jbalia , Abdessatar Khelifi

We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $\Omega$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass density $v(x,t)$ for $x\in\Omega$ and…

Analysis of PDEs · Mathematics 2026-03-31 Xinyue Luo , Masahiro Yamamoto , Jin Cheng

In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…

Analysis of PDEs · Mathematics 2024-12-12 Kuang Huang , Bangti Jin , Yavar Kian , Georges Sadaka , Zhi Zhou

This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed…

Analysis of PDEs · Mathematics 2025-01-16 Julieta Bollati , Ernesto A. Borrego Rodriguez , Adriana C. Briozzo , Colin Rogers

From the one-dimensional consolidation of fine-grained soils with threshold gradient, it can be derived a special type of Stefan problems where the seepage front, due to the presence of this threshold gradient, exhibits the features of a…

Analysis of PDEs · Mathematics 2017-03-24 Julieta Bollati , Domingo A. Tarzia

This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…

Analysis of PDEs · Mathematics 2022-12-28 S. E. Chorfi , G. El Guermai , L. Maniar , W. Zouhair

This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…

Optimization and Control · Mathematics 2008-09-23 Jesper Carlsson

To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…

Numerical Analysis · Mathematics 2025-07-11 Yunqing Huang , Shihan Zhang

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

In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem,…

Analysis of PDEs · Mathematics 2018-08-09 Julieta Bollati , José A. Semitiel , Domingo A. Tarzia

This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…

Analysis of PDEs · Mathematics 2019-02-20 De-Han Chen , Yousept Irwin , Jun Zou

We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that…

Analysis of PDEs · Mathematics 2023-03-06 Jørgen Endal , Liviu I. Ignat , Fernando Quirós

The detailed mathematical model of heat and mass transfer of steel ingot of curvilinear continuous casting machine is proposed. The process of heat and mass transfer is described by nonlinear partial differential equations of parabolic…

Optimization and Control · Mathematics 2010-03-25 Anna Ivanova