THE EXISTENCE OF SOLUTION OF HYPERBOLIC EQUATION IN  ,  p l l L R d x SPACE, THE COUCHY PROBLEM FOR HYPERBOLIC EQUATIONS - Yremenko, M. I. (Computer Science and Applied Mathematics, 2016)
Dedicated to the research of the conditions of existence of the solution of the Cauchy problem for hyperbolic equations in Lebesgue space. We conducted the research under the scheme: by the equation we built a special form and studied its properties, has its boundedness established this form creates an operator and we study the properties of the operator using the form that it generates. Then we have a theorem on the existence of the solution of the equation by which the form is built. To proof the theorem Galerkin scheme is being used, we built Galerkin sequence of approximation and showed that this sequence converges to the solution of the hyperbolic equation.