Research output: Contribution to journal › Article › peer-review
The Heat Transfer Equation with an Unknown Heat Capacity Coefficient. / Kozhanov, A. I.
In: Journal of Applied and Industrial Mathematics, Vol. 14, No. 1, 20.03.2020, p. 104-114.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 23895703