Related papers: Uniqueness of Inverse Source Problems for General …
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
In this work, we consider an inverse potential problem in the parabolic equation, where the unknown potential is a space-dependent function and the used measurement is the final time data. The unknown potential in this inverse problem is…
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…
This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…
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…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
This paper is concerned with the uniqueness on two inverse moving source problems in electrodynamics with partial boundary data. We show that (1) if the temporal source function is compactly supported, then the spatial source profile…
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse…
We prove the well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter $t$ on top of…
We consider a diffusion and a wave equations: $$ \partial_t^ku(x,t) = \Delta u(x,t) + \mu(t)f(x), \quad x\in \Omega, \, t>0, \quad k=1,2 $$ with the zero initial and boundary conditions, where $\Omega \subset \mathbb{R}^d$ is a bounded…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
This paper is concerned with identification of a spatial source function from final time observation in a bi-parabolic equation, where the full source function is assumed to be a product of time dependent and a space dependent function. Due…
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…
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…
This article is concerned with the derivation of numerical reconstruction schemes for the inverse moving source problem on determining source profiles in (time-fractional) evolution equations. As a continuation of the theoretical result on…
We study formally determined inverse problems with passive measurements for one dimensional evolution equations where the goal is to simultaneously determine both the initial data as well as the variable coefficients in such an equation…
This article is devoted to inverse problems of recovering point sources in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of these inverse problems with pointwise overdetermination…
We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order $\alpha \in (0,1)$ which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse…
In the present paper, we investigate the initial-boundary value problem for fractional order parabolic equation on a metric star graph in Sobolev spaces. First, we prove the existence and uniqueness results of strong solutions which are…