V. B. Dmitriev, “A mixed problem with nonlinear integral condition for a hyperbolic equation”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2009, Issue 6(72),Pages <nobr>35

Mathematics

A mixed problem with nonlinear integral condition for a hyperbolic equation

V. B. Dmitriev

Dept. of Mathematical Methods and Information Technologies, Samara Municipal Management Institute, Samara, 443084, Russia

Abstract: Mixed problem for the hyperbolic equation with non-linear integral condition instead of a standard boundary condition and non-linear right side is viewed in the work. The task is viewed in the space of arbitrary dimensionality. The existence and uniqueness of the solution is proved.

Keywords: nonlocal problem, hyperbolic equation, apriori estimation, generalized solution.

UDC: 517.956.3

Received: 22.06.2009
Revised: 22.06.2009