Open AccessINVERSE PROBLEMS IN THE HEAT AND MASS TRANSFER THEORY
Author(s) -
Sergey Grigorievich Pyatkov
Publication year - 2017
Publication title -
vestnik ûgorskogo gosudarstvennogo universiteta
Language(s) - English
Resource type - Journals
eISSN - 2078-9114
pISSN - 1816-9228
DOI - 10.17816/byusu20170461-78
Subject(s) - uniqueness , inverse problem , mathematics , sobolev space , overdetermination , stability (learning theory) , inverse , heat equation , function (biology) , diffusion , space (punctuation) , mathematical analysis , computer science , physics , philosophy , geometry , epistemology , machine learning , evolutionary biology , biology , operating system , thermodynamics
This article is a survey of the recent results obtained preferably by the author and its coauthors and devoted to the study of inverse problem for some mathematical models, in particular those describing heat and mass transfer and convection-diffusion processes. They are defined by second and higher order parabolic equations and systems. We examine the following two types of overdetermination conditions: a solution is specified on some collection of spatial manifolds (or at separate points) or some collection of integrals of a solution with weight is prescribed. We study an inverse problem of recovering a right-hand side (the source function) or the coefficients of equations characterizing the medium. The unknowns (coefficients and the right-hand side) depend on time and a part of the space variables. We expose existence and uniqueness theorems, stability estimates for solutions. The main results in the linear case, i.e., we recover the source function, are global in time while they are local in time in the general case. The main function spaces used are the Sobolev spaces.