On some properties of a system of nonlinear partial functional differential equations

Abstract

We consider a system of a semilinear hyperbolic functional differential equation (where the lower order terms contain functional dependence on the unknown function) with initial and boundary conditions and a quasilinear elliptic functional differential equation (containing $t$ as a parameter) with boundary conditions. Existence and some qualitative properties of weak solutions for $t\in (0,\infty )$ are proved.

Keywords

• partial functional-differential equations
• nonlinear systems of partial differential equations
• nonlinear systems of mixed type
• qualitative properties