Optimal Lp(1≤p≤∞) rates of decay to linear diffusion waves for nonlinear evolution equations with ellipticity and dissipation

In this paper, we are concerned with the large time decay estimates of solutions to the Cauchy problem of nonlinear evolution equations with ellipticity and damping. Different end states of initial data are considered. The optimal rate of decay to the linear diffusion waves is obtained. The optimal rate of decay of solutions to the linearized system plays a crucial role in the analysis.