DOI: https://doi.org/10.36719/2663-4619/117/145-150
Hamida Aghayeva
Baku State University
https://orcid.org/0009-0001-8928-6433
hamidaagayeva5@gmail.com
On the Formal Solution of a Mixed Problem
Abstract
The paper considers the formal solution of a mixed problem with regular boundary conditions for a parabolic differential equation describing the heat transfer equation. The existence and basic properties of the Green's function are studied based on spectral analysis. Using the Fourier transform and the residue method, the solution is expressed as a non-specific integral expansion. It is proved that the obtained formal expression satisfies the given initial and boundary conditions, and the uniqueness of the solution is shown.
Finally, it is proved that the obtained formal solution fully satisfies the given initial and boundary conditions. In addition, the uniqueness of the constructed formal solution is mathematically justified, and this result shows that the problem has a correct solution. Thus, the solution obtained for the mixed problem given in the article is obtained by an approach that is both mathematically justified and provides important results from an applied point of view.
Keywords: mixed problem, method of deductions, regular boundary conditions, Green's function