Nonlocal problems for hyperbolic equations from the viewpoint of strongly regular boundary conditions

Abstract

In this article, we consider a nonlocal problem for hyperbolic equation with integral conditions and show their close connection with the notion of strongly regular boundary conditions. This has an important bearing on the method of the study of solvability. We propose also a new approach which enables us to prove a unique solvability of the nonlocal problem with integral condition.

Keywords

• nonlocal problem
• hyperbolic equation
• nonlocal integral conditions
• dynamical boundary conditions
• strongly regular boundary conditions
• weak solution