Existence of solutions to higher order semilinear hyperbolic equations with damping term

Abstract

In this paper, we study the existence and uniqueness of the initial and boundary value problem for a class of higher order semilinear hyperbolic partial differential equations with damping term. Based on priori estimates of solution we proved the existence of the weak solution in the form of Fourier series under suitable conditions. For this purpose Picard's successive approximation method was used. Furthermore we proved the uniqueness of the weak solution.