This article is cited in 1 paper

The first boundary problem with an integral condition for a mixed-type equation with a characteristic degeneration

Yu. K. Sabitova<sup>ab

a</sup> Sterlitamak Branch of Bashkir State University, 49 Lenin Ave., Sterlitamak, 453100 Russia
^b Sterlitamak branch of the Institute for strategic studies of the Republic of Bashkortostan, 68 Odesskaya str., Sterlitamak, 453103 Russia

Abstract: For a mixed equation of elliptic-hyperbolic type in rectangular domain the first boundary problem is investigated. The criterion of uniqueness is established. The solution of the problem is constructed in the form of the sum of a biorthogonal row. Small denominators are appeared in process of proving existence of the solution of the problem. The estimates about a remoteness from zero denominators are established with the corresponding assymptotics which allowed to prove existence of the decision in a class of regular decisions and prove its stability depending on boundary functions.

Keywords: a equation of mixed type, a characteristic degeneration, Dirikhle's problem, criterion of uniqueness, existense, a biorthogonal row, small denominators, stability.

UDC: 517.95

Received: 05.12.2019
Revised: 05.12.2019
Accepted: 25.03.2020

DOI: 10.26907/0021-3446-2020-11-46-64

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:11, 39–57

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