TY - JOUR

T1 - The Heat Transfer Equation with an Unknown Heat Capacity Coefficient

AU - Kozhanov, A. I.

PY - 2020/3/20

Y1 - 2020/3/20

N2 - Under study are the inverse problems of finding, together with a solution u(x,t) of the differential equation cut − Δu + a(x, t)u = f(x, t) describing the process of heat distribution, some real c characterizing the heat capacity of the medium (under the assumption that the medium is homogeneous). Not only the initial condition is imposed on u(x, t), but also the usual conditions of the first or second initial-boundary value problems as well as some special overdetermination conditions. We prove the theorems of existence of a solution (u(x, t), c) such that u(x, t) has all Sobolev generalized derivatives entered into the equation, while c is a positive number.

AB - Under study are the inverse problems of finding, together with a solution u(x,t) of the differential equation cut − Δu + a(x, t)u = f(x, t) describing the process of heat distribution, some real c characterizing the heat capacity of the medium (under the assumption that the medium is homogeneous). Not only the initial condition is imposed on u(x, t), but also the usual conditions of the first or second initial-boundary value problems as well as some special overdetermination conditions. We prove the theorems of existence of a solution (u(x, t), c) such that u(x, t) has all Sobolev generalized derivatives entered into the equation, while c is a positive number.

KW - existence

KW - final-integral overdetermination conditions

KW - heat capacity coefficient

KW - heat transfer equation

KW - inverse problem

UR - http://www.scopus.com/inward/record.url?scp=85081998462&partnerID=8YFLogxK

U2 - 10.1134/S1990478920010111

DO - 10.1134/S1990478920010111

M3 - Article

AN - SCOPUS:85081998462

VL - 14

SP - 104

EP - 114

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -