Regularity properties of integral problems for wave equations and applications

Abstract

In this paper, the integral problem for linear and nonlinear wave equations are studied.The equation involves elliptic operator L and abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data in terms of interpolation spaces, integral condition, the assumptions on operators A, L the existence, uniqueness of local and global solution, and Lp-regularity properties to solutions are established. By choosing the space H and operators L, A the regularity properties to solutions of different classes of wave equations in the field of physics are obtained.