The dirichlet problem for an equation of mixed elliptic-hyperbolic type with variable potential

被引：1

作者：

Martem’yanova N.V. ^{[1
]}

机构：

[1] Volga Region Social-Humanitarian Academy, ul. Antonova-Ovseenko 26, Samara

来源：

Russian Mathematics | 2015年 / 59卷 / 11期

关键词：

Dirichlet problem; existence; mixed type equation; small denominators; spectral method; uniqueness;

D O I：

10.3103/S1066369X15110043

中图分类号：

学科分类号：

摘要：

We study the Dirichlet problem for an equation of mixed elliptic-hyperbolic type with variable potential in the rectangular area. We establish a criterion of the uniqueness of a solution to this problem. The uniqueness of a solution is proved on the basis of the completeness of systems of functions corresponding to one-dimensional spectral problem. Solutionwas constructed as a sumof series on the systems of eigenfunctions. The existence is proved under certain conditions on the ratio of the rectangle sides of hyperbolic part of the equation, upon the boundary functions and function of potential. © 2015, Allerton Press, Inc.

引用

页码：36 / 44

页数：8

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