Solution of boundary value problems for the heat equation with a piecewise constant coefficient using the Fourier method
Year: 2024
Type: article
Abstract: This paper considers some initial boundary value problems for the heat equation in a bounded segment with a piecewise constant coefficient. Using the method of separation of variables, the problem under consideration is reduced to a spectral problem and eigenvalues and eigenfunctions of the resulting spectral problem are found. It is shown that the system of eigenfunctions forms a Riesz basis. Next, we prove a theorem on the existence and uniqueness of solutions to the initial-boundary value problems under consideration.
Source: Kazakh mathematical journal.
DOI: 10.70474/drms4076
Authors: Umbetkul Koilyshov, Makhmud Sadybekov
Institution: Institute of Mathematics and Mathematical Modeling
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4404482162