Related papers: Inverse Stefan problems of determining the time-de…
This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
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…
We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in…
Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…
In this article, We investigate an inverse problem of determining the time-dependent source factor in parabolic integro-differential equations from boundary data. We establish the uniqueness and the conditional stability estimate of…
Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is…
In this paper we consider two different Stefan problems for a semi-infinite material for the non classical heat equation with a source which depends on the heat flux at the fixed face x = 0. One of them (with constant temperature on x = 0)…
We address the inverse problem of identifying a time-dependent source coefficient in a one-dimensional heat equation with a fractional Laplacian subject to Dirichlet boundary conditions and an integral nonlocal data. An a priori estimate is…
This paper explores the forward and inverse problems for a fractional subdiffusion equation characterized by time-dependent diffusion and reaction coefficients. Initially, the forward problem is examined, and its unique solvability is…
The heat transfer model for a one-dimensional supercooled melt during the final stage of solidification is considered. The Stefan problem for the determination of the temperature distribution is solved under the condition that (i) the…
This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…
We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems…
In this paper, we study the control of the linear heat equation with a space and time dependent coefficient function by the Dirichlet and Neumann boundary control laws. This equation models the heat diffusion and space, time dependent heat…
The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies…
In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component is…
In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear…
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…
In this paper, we deal with the inverse source problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution does not depend continuously on the…