Two-phase heat conduction problems with Sturm-type boundary conditions
Koilyshov U. Sadybekov M.
December 2024Springer Science and Business Media Deutschland GmbH
Boundary Value Problems
2024#2024Issue 1
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.
35A09 , 35L20 , 35M13 , Discontinuous coefficients , Eigenfunctions , Eigenvalues , Heat conduction equation , Method of separation of variables
Text of the article Перейти на текст статьи
Department of differential equations, Institute of Mathematics and Mathematical Modeling, Pushkin, Almaty, Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, al-Farabi, Almaty, 050040, Kazakhstan
Department of differential equations
Al-Farabi Kazakh National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026