Semilinear hyperbolic functional differential problem on a cylindrical domain

Abstract

We consider the initial boundary value problem for a semi-linear partial functional differential equation of the first order on a cylindrical domain in $n+1$ dimensions. Projection of the domain onto the $n$-dimensional hyperplane is a connected set with boundary satisfying certain type of cone condition. Using the method of characteristics and the Banach contraction theorem, we prove the global existence, uniqueness and continuous dependence on data of Carathéodory solutions of the problem. This approach cover equations with deviating variables as well as differential integral equations.