Electron. J. Diff. Equ., Vol. 2016 (2016), No. 193, pp. 1-12.

Nonlocal problems for hyperbolic equations with degenerate integral conditions

Ludmila S. Pulkina

Abstract:
In this article, we consider a problem for hyperbolic equation with standard initial data and nonlocal condition. A distinct feature of this problem is that the nonlocal second kind integral condition degenerates and turns into a first kind. This has an important bearing on the method of the study of solvability. All methods worked out earlier for this purpose break down in the case under consideration. We propose a new approach which enables to prove a unique solvability of the nonlocal problem with degenerate integral condition.

Submitted May 12, 2016. Published July 15, 2016.
Math Subject Classifications: 35L10, 35L20, 35L99.
Key Words: Nonlocal problem; hyperbolic equation; integral condition; dynamical boundary condition; degenerate integral condition.

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Ludmila S. Pulkina
Samara University
Samara, Russia
email: louise@samdiff.ru

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