An inverse diffusion problem with nonlocal boundary conditions

Abstract

This article considers the inverse problem of identification of a time-dependent thermal diffusivity together with the temperature in an one-dimensional heat equation with nonlocal boundary and integral overdetermination conditions when a heat exchange takes place across boundary of the material. The well-posedness of the problem is studied under some regularity, and consistency conditions on the data of the problem together with the nonnegativity condition on the Fourier coefficients of the initial data and source term. The inverse problem is also studied numerically by using the Crank-Nicolson finite difference scheme combined with predictor-corrector technique. The numerical examples are presented and discussed.

Mathematical Approach to Solving the Problem of Waste-Free Processing of Metallurgical Wastes

“…The target output variables selected are: residual metal recovery rate and physicochemical features of expanded claydite [43,44].…”

“…Usually the following "elementary" processes are considered when modeling chemical technology objects: movement of phase flows; mass transfer between phases; heat transfer; change of aggregate state; chemical transformations. The application of mathematical methods in solving technological problems allows to raise the general level of theoretical research and makes it possible to conduct it in closer connection with experimental research [40][41][42][43][44].…”

A source inverse problem for the pseudo–parabolic equation with the fractional Sturm–Liouville operator

“…When α = 1, Shauder's fixed point theorem is used in many works, here we only note a few of them [I93,KI12,IO16,HLI16]. To the best of our knowledge, in this paper we use Shauder's fixed point theorem to prove the existence of the solution to the obtained operator equation for the first time.…”