This article is cited in 7 papers

Dirichlet problem for Lavrent'ev–Bitsadze equation with loaded summands

Yu. K. Sabitova<sup>ab

a</sup> Sterlitamak Branch of Bashkir State University, 49 Lenin Ave., Sterlitamak, 453100 Russia
^b Institute of Strategic Studies of Bashkortostan Republic, Sterlitamak Branch

Abstract: We study the first boundary-value problem for loaded equation of elliptic-hyperbolic type in rectangular domain. We establish a criterion of uniqueness. A solution to the problem is constructed in the form of the sum of a series. In substantiation of existence of a solution to a problem small denominators appear. We obtain the estimates about a separation from zero of denominators with the corresponding asymptotics. They allow to prove existence of a solution in a class of regular solutions.

Keywords: loaded equation of mixed type, Dirichlet's problem, criterion of uniqueness, existence, series, small denominator, estimate, uniform convergence.

UDC: 517.95

Received: 02.05.2017

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:9, 35–51

Bibliographic databases:

• 
•