Integral Analogue of the First Initial-Boundary Value Problem for Second-Order Hyperbolic and Parabolic Equations

被引：0

作者：

Kozhanov, A., I ^{[1
,2
]}

Dyuzheva, A., V ^{[2
]}

机构：

[1] Russian Acad Sci, Sobolev Inst Math, Siberian Branch, Novosibirsk 630090, Russia

[2] Samara State Tech Univ, Samara 443100, Russia

来源：

MATHEMATICAL NOTES | 2022年 / 111卷 / 3-4期

关键词：

second-order hyperbolic and parabolic equations; nonlocal problems; integral analogue of the first initial-boundary value problem; regular solutions; existence; uniqueness; SOLVABILITY;

D O I：

10.1134/S0001434622030245

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the solvability of initial-boundary value problems for second-order hyperbolic and parabolic equations with a boundary condition that integrally connects the values of the solution on the lateral boundary with the values of the solution inside the domain. To study such problems, it was previously established that their solvability is ensured by the bijectivity of a certain Fredholm operator constructed from an integral condition. In this paper, we show that the condition of predecessors is not required for the existence and uniqueness of regular solutions (solutions with all derivatives generalized in the sense of Sobolev that are contained in the equation) of integral analogues of the first initial-boundary value problem for second-order hyperbolic and parabolic equations.

引用

页码：562 / 570

页数：9

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