A problem with a nonlocal, with respect to time, condition for multidimensional hyperbolic equations

被引：12

作者：

Pul’kina L.S. ^{[1
]}

Savenkova A.E. ^{[2
]}

机构：

[1] Samara National Research University named after Academician S. P. Korolyov, Moskovskoe sh. 34, Samara

[2] Samara Technical State University, ul. Molodogvardeiskaya 244, Samara

来源：

Russian Mathematics | 2016年 / 60卷 / 10期

关键词：

generalized solution; hyperbolic equation; integral conditions; nonlocal problem;

D O I：

10.3103/S1066369X16100066

中图分类号：

学科分类号：

摘要：

We study a boundary-value problem for a hyperbolic equation with a nonlocal with respect to time-variable integral condition. We obtain sufficient conditions for unique solvability of the nonlocal problem. The proof is based on reduction of the nonlocal first-type condition to the second-type one. This allows to reduce the nonlocal problem to an operator equation. We show that unique solvability of the operator equation implies the existence of a unique solution to the problem. © 2016, Allerton Press, Inc.

引用

页码：33 / 43

页数：10

共 14 条

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