Nonlocal problems for hyperbolic equations with degenerate integral conditions

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.

Keywords

• Nonlocal problem
• hyperbolic equation
• integral condition
• dynamical boundary condition
• degenerate integral condition