An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition

Abstract

In this paper, the inverse problem of finding the time‐dependent coefficient of heat capacity together with the solution periodic boundary and integral overdetermination conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness, and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example. Copyright © 2014 John Wiley & Sons, Ltd.

A numerical solution of an inverse diffusion problem based on operational matrices of orthonormal polynomials

“…A number of papers presented the study of the coefficient inverse problems concerning the heat equation with the integral boundary conditions. [38][39][40][41][42] In these papers, the authors addressed some natural regularity and consistency conditions on the input data under which the existence, uniqueness, and continuous dependence upon the data of the solution were shown and then the finite difference method (FDM) was applied to solve the problem. In Zhou et al, 43 authors applied the variational iteration method to present the analytical solution of some inverse problem of recovering the time or space-dependent coefficients.…”

“…The interested reader can refer to previous studies 34–37 and many other references therein for a summary of numerical solutions to parabolic problems with nonlocal boundary conditions. A number of papers presented the study of the coefficient inverse problems concerning the heat equation with the integral boundary conditions 38–42 . In these papers, the authors addressed some natural regularity and consistency conditions on the input data under which the existence, uniqueness, and continuous dependence upon the data of the solution were shown and then the finite difference method (FDM) was applied to solve the problem.…”

Fourier method for higher dimensional inverse quasi‐linear parabolic problem

“…Inverse parabolic problems in two dimensional are appeared especially applications in chemical diffusion, heat transfer processes have been used a lot such as [1,5], population, medical area, electrochemistry, engineering, chemical area, and plasma physics [3]. This kind of problems with nonlocal boundary conditions are not easy to study.…”

“…Finding of the unknown function in a nonlinear parabolic equation is used frequently by many engineers and scientists [1,4,[6][7][8].…”

Inverse problem for Euler-Bernoulli equation with periodic boundary condition

“…[6,7] studied non-local boundary value problems and concluded that the presence of integral terms in boundary conditions can greatly complicate the application of standard numerical techniques such as finite difference schemes, finite element techniques etc. [2,11,12] The periodic conditions are used on lunar theory [9]. In heat propagation in a thin rod in which the law of variation E(t) of the total quantity of heat in the rod is given in [10].…”