Initial-Boundary Problem for Parabolic-Hyperbolic Equation with Loaded Summands

被引：21

作者：

Sabitov, K. B. ^{[1
,2
]}

机构：

[1] Volga Reg Social Humanitarian Acad, Ul Antonova Ovseenko 26, Samara 443090, Russia

[2] Inst Appl Res Republ Bashkortostan, Sterlitamak 453103, Russia

来源：

RUSSIAN MATHEMATICS | 2015年 / 59卷 / 06期

关键词：

mixed-type equation with loaded summands; initial-boundary problem; uniqueness; existence; stability;

D O I：

10.3103/S1066369X15060055

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we find necessary and sufficient conditions for uniqueness of solution to the initial-boundary problem for a loaded equation of mixed parabolic-hyperbolic type. The solution is constructed as a sum of a series in eigenfunctions of the corresponding one-dimensional problem on eigenvalues. In the proof of convergence of the series the problem of small denominators arises. Under certain conditions on these problems we obtain an estimate for a small denominator to be separated from zero that allows to prove the existence theorem in the class of regular solutions.

引用

页码：23 / 33

页数：11

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