A semilinear integro-differential equation: global existence and hidden regularity

Abstract

Here we show a hidden regularity result for nonlinear wave equations with an integral term of convolution type and Dirichlet boundary conditions. Under general assumptions on the nonlinear term and on the integral kernel we are able to state results about global existence of strong and mild solutions without any further smallness on the initial data. Then we define the trace of the normal derivative of the solution showing a regularity result. In such a way we extend to integrodifferential equations with nonlinear term well-known results available in the literature for linear wave equations with memory.