Long‐time asymptotics via entropy methods for diffusion dominated equations

Abstract

Uniform convergence rates of diffusion dominated equations towards their asymptotic profiles are quantified via entropy methods for bounded integrable non‐negative initial data with finite entropy. Convergence rates are sharp since they coincide with the purely diffusive ones. The approach is applied to both convection– and absorption–diffusion equations. Finally, Wasserstein metrics are used to control the expansion of the support for the convection–diffusion case.