A note on decay properties for the solutions of a class of partial differential equation with memory

摘要

The purpose of this article is to study decay properties for solutions of a class of PDEs with memory by Lyapunov functionals method. Moreover, we prove that when the kernels of the convolutions decay exponentially, the first and second order energy of the solutions decay exponentially. Also we show that when the kernels decay polynomially, these energies decay polynomially.