On a Nonlinear Degenerate Evolution Equation with Nonlinear Boundary Damping

Abstract

This paper deals essentially with a nonlinear degenerate evolution equation of the form Ku″-Δu+∑j=1nbj∂u′/∂xj+uσu=0 supplemented with nonlinear boundary conditions of Neumann type given by ∂u/∂ν+h·, u′=0. Under suitable conditions the existence and uniqueness of solutions are shown and that the boundary damping produces a uniform global stability of the corresponding solutions.