Two-phase heat conduction problems with Sturm-type boundary conditions

Umbetkul Кoilyshov, Makhmud Abdysametovich Sadybekov

Boundary Value Problems, 2024

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DOI 10.1186/s13661-024-01964-x

Data confidence 70 medium

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Abstract

Abstract In this work, the solution is justified using the method of separation of variables for initial-boundary value problems of the heat conduction equation with piecewise constant thermal conductivity coefficient under Sturm-type boundary conditions (separated boundary conditions). Various cases are considered. A system of eigenfunctions of the corresponding spectral problem is constructed and it is proved that this system of eigenfunctions forms a Riesz basis. The theorem of the existence of a unique classical solution to the problem is proved.