On a system of nonlinear partial functional differential equations of different types

Abstract

We consider a system of a semilinear hyperbolic functional differential
equation (where the lower order terms contain functional
dependence on the unknown function) and a quasilinear parabolic
functional differential equation with initial and boundary
conditions. Existence of weak solutions for $t\in (0,T)$ and for
$t\in (0,\infty )$ will be shown and some qualitative properties
of the solutions in $(0,\infty )$ will be formulated.