Dirichlet Problem for Lavrent’ev–Bitsadze Equation With Loaded Summands
Yu. K. SabitovaSterlitamak Branch of Bashkir State University; Sterlitamak Branch of Institute for Strategic Research of Bashkortostan Republic, pr. Lenina 49, Sterlitamak, 453100, Russia
2018en
ABI
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 formof 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.
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Cited by 20 references