Solvability of a nonlocal problem for a hyperbolic equation with degenerate integral conditions

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki

Ludmila Stepanovna Pulkina¹  Vitaliya Aleksandrovna Kirichek¹ 

[1] Samara National Research University;

关键词: hyperbolic equation;    nonlocal problem;    1st and 2d kind integral conditions;    degenerate nonlocal conditions;    dynamical boundary conditions;    generalized solution;    sobolev space;   

DOI  :  10.14498/vsgtu1707

来源: DOAJ

【 摘 要 】

In this paper, we consider a nonlocal problem with integral conditions for hyperbolic equation. Close attention focuses on degenerate integral conditions, namely, on the second kind integral conditions which degenerate into the first kind conditions at some points. Such kind of nonlocal conditions inevitably involves some specific difficulties when we try to show solvability of the problem. These difficulties can be overcome by a method suggested in our paper. The essence of this method is the reduction of the problem with degenerate conditions to the problem with dynamical conditions. This technique enables to define effectively a generalized solution to the problem, to obtain a priori estimates and to prove the existence of a unique generalized solution to the problem.

【 授权许可】

Unknown