Abstract:
In this paper we consider a problem for hyperbolic equation with integral conditions of the second kind containing as non-integral terms values of required solution on lateral boundary. Nonlocal conditions of this kind generate significant difficulties in the study of the solvability of the problem. But these difficulties were overcome and existence the only solution to the problem is proved. The main tool for proving this statement is a priori estimates in Sobolev spaces, the obtaining of which became possible as a result of applying the method developed for the case of a one-dimensional hyperbolic equation.
Keywords:hyperbolic equation, nonlocal problem, integral conditions, weak solution, Sobolev spaces.
