Energy decay for a weakly nonlinear damped porous system with a nonlinear delay

Abstract

This paper considers a one-dimensional porous system damped with weakly nonlinear feedback in the presence of a nonlinear delay. We prove the global existence and uniqueness results using the Faedo–Galerkin procedure. Furthermore, under appropriate assumptions on the weight of the delay and without imposing any restrictive growth assumption on the damping term at the origin, we establish an energy decay rate, using a perturbed energy method and some properties of convex functions in case of the same speed of propagation in the two equations of the system.