The Energy Decay Estimates Of Solutions For Nonlinear Equations With Memory Kernels

This paper has studied the energy decay estimates of solutions for a first order Cahn-Hilliard equation under the dynamic boundary conditions and a type of second order viscoelastic equation under the clamped boundary condi-tions, by means of constructing some suitable energy functionals and applying some differential inequalities, we studied the energy decay manners of solutions for these two types of equations when the memory kernels satisfied a certain de-cay condition.