The Lp -regularity properties of nonlocal wave equations and applications

Abstract

In this paper, the Cauchy problem for linear and nonlinear wave equations is studied. The equation involves abstract operator A in a Banach space E and convolution terms. Here, assuming enough smoothness on the initial data and on coefficients, the existence, uniqueness and regularity properties of local and global solutions are established in terms of fractional powers of a given sectorial operator A. We obtain the regularity properties of a wide class of wave equations by choosing the space E and the operator A which appear in the field of physics.