ON THE SOLVABILITY OF A NONLOCAL PROBLEM FOR A TWO-DIMENSIONAL DIFFUSION EQUATION WITH INVOLUTION

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Abstract

This work is devoted to the study of the solvability of a nonlocal problem for a two-dimensional heat equation with involution. The problem is solved by reducing it to two equivalent problems for the classical two-dimensional heat equation. The properties of the system of eigenfunctions and associated functions of the spectral problem associated with nonlocal conditions are studied. The theorem on the existence and uniqueness of the solution is proved. The solution to the problem is represented in the form of a Fourier series.