The Heat Transfer Equation with an Unknown Heat Capacity Coefficient

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Abstract

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.

Original languageEnglish
Pages (from-to)104-114
Number of pages11
JournalJournal of Applied and Industrial Mathematics
Volume14
Issue number1
DOIs
Publication statusPublished - 20 Mar 2020

Keywords

  • existence
  • final-integral overdetermination conditions
  • heat capacity coefficient
  • heat transfer equation
  • inverse problem

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