Mathematics

On one problem with dynamic nonlocal condition for a hyperbolic equation

A. E. Savenkova

Samara State University, 1, Acad. Pavlov Street, Samara, 443011, Russian Federation

Abstract: In this article, boundary value problem for hyperbolic partial differential equation with nonlocal data in an integral of the second kind form is considered. The emergence of dynamic conditions may be due to the presence of a damping device. Existence and uniqueness of generalized solution is proved in a given cylindrical field. There is some limitation on the input data. The uniqueness of generalized solution is proved by apriori estimates. The existence is proved by Galerkin’s method and embedding theorems.

Keywords: hyperbolic equation, dynamic nonlocal conditions, nonlocal condition of the second kind, integral conditions, generalized solution, Galerkin method, damping device, dynamic boundary conditions.

UDC: 517.956

Received: 15.03.2015

Bibliographic databases:

•