The nonlocal A. A. Desin's problem for an equation of mixed elliptichyperbolic type

Abstract

In this paper for the equation of mixed elliptic-hyperbolic type in rectangular area the task with the conditions of periodicity and the nonlocal problem of A. A. Desin was studied, the uniqueness criterion was set. The solution of the problem was constructed as a sum of orthogonal series in eigenfunctions of the corresponding one-dimensional spectral problem. The problem of small denominators arises in justifying the convergence of the series. Therefore the evaluation on the separation from zero of small denominators with the corresponding asymptotics was established. This assessment allowed under certain conditions relative to the set objectives and functions to prove convergence of the constructed series in the class of regular solutions and the stability of the solution.

Keywords

• equation of mixed type nonlocal problem
• uniqueness criterion
• the existence
• series
• small denominators
• stability