A Boundary Value Problem with Conditions on the Entire Boundary of a Noncharacteristic Domain for a Fourth-Order Equation

被引：1

作者：

Utkina, E. A. ^{[1
]}

机构：

[1] Kazan Fed Univ, Kazan 420008, Tatarstan, Russia

来源：

DOKLADY MATHEMATICS | 2011年 / 84卷 / 01期

关键词：

Unique Solvability; Zero Solution; Order Partial Differential Equation; Entire Boundary; Longitudinal Wave;

D O I：

10.1134/S1064562411030434

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A boundary value problem with conditions on the entire boundary of a noncharacteristic domain for a fourth-order equation is studied. A method for obtaining conditions which ensure the unique solvability of this problem is proposed. This method reduces the problem to Fredholm equations, whose unique solvability is ensured by a uniqueness theorem proved by the method. To prove the uniqueness of a solution to problem, it is verified that under homogeneous conditions, the homogeneous equation has only the zero solution. The function, which is not identically zero on the domain, is a solution to the problem.

引用

页码：539 / 541

页数：3

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