SOLVABILITY OF A MIXED PROBLEM FOR A DEGENERATE SUB-DIFFUSION EQUATION IN A RECTANGULAR DOMAIN (Scientific journal of the Fergana State University, 2026)
In the present paper, a mixed boundary value problem for a degenerate sub-diffusion equation in a rectangular domain is studied. By applying the method of separation of variables, a spectral problem for a space-dependent ordinary differential equation is derived. The existence of eigenvalues and eigenfunctions of the resulting spectral problem is established using the theory of positive differential operators. The solution to the problem is constructed in the form of a Fourier series. The convergence of the obtained series is proved, and the uniqueness of the solution is established by exploiting the completeness of the system of eigenfunctions.