ЗАДАЧА С ГРАНИЧНЫМ УСЛОВИЕМ ВТОРОГО РОДА ДЛЯ УРАВНЕНИЯ ЭЛЛИПТИКО-ГИПЕРБОЛИЧЕСКОГО ТИПА В ПРЯМОУГОЛЬНО̆Й ОБЛАСТИ - Кылышбаева, Г.К. (SCIENCE and SOCIETY, 2024)
In this paper we propose a method for solving the Dirichlet-type problem for a third-order elliptic-hyperbolic equation with a boundary condition of the second kind in a rectangular region. It is shown that the correctness of the problem formulation essentially depends on the ratio of the sides of the rectangle from the hyperbolic part of the mixed region. The solution of the problem in the form of a sum of series on eigenfunctions of the corresponding one-dimensional spectral problem is constructed. The criterion of singularity of the solution is established. Estimates of stability of the solution from the given boundary functions are proved.
Keywords: third order equation; Dirichlet-type problem; small denominators; uniqueness; existence and stability of the solution