Dirichlet and Poincare in the multidimensional field for a class of singular hyperbolic equations

Abstract

It has been shown in a plane that one of fundamental problems of Math Physics, i.e. studying the behavior of a hesitating string, is not correct when boundary conditions are given on the whole boundary of the domain. As it is shown below, Dirichlet problem is incorrect not just for a wave equation but for general hyperbolic equations. In the works of the author studied the Dirichlet and Poincar? problem for linear multidimensional hyperbolic equations, which shows the correctness of these tasks, depending essentially on the height of the considered cylindrical domain.In this paper we find multi-dimensional area in which the Dirichlet and the Poincare problem solved for a class of singular hyperbolic equations.