The Heat Transfer Equation with an Unknown Heat Capacity Coefficient

Результат исследования: Научные публикации в периодических изданияхстатья

1 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)104-114
Число страниц11
ЖурналJournal of Applied and Industrial Mathematics
Том14
Номер выпуска1
DOI
СостояниеОпубликовано - 20 мар 2020

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