BOUNDARY VALUE PROBLEMS FOR A FOURTH ORDER HYPERBOLIC EQUATION IN PARTIAL DERIVATIVES

Abstract

           The subject of the study is well-posed boundary valye problems for high-order differential equations. The purpose of this paper is to study weii-posed boundary value problems for a fourth-order hyperbolic partial differential equation. The studyuses the methods of integrals, which helping the uniqueness of the solution of the problem is proved. The existence and uniqueness of the solution of the first boundary value problem for a fourth-order hyperbolic equation with a variable coefficient is proved Scientific and practical value: By lowering the order of the equation, the problem is reduced a boundary value problem for a second-order differential equation. A representation of the solution of the problem in terms of Green’s functions is obtained Examples are given in the case when the coefficient is zero and negative. It is shown that at what values of the coefficient, the uniqueness of the solution of the problem is violated. The results obtained can be used in teaching students of mathematical specialties.