Long-time asymptotics via entropy methods for diffusion dominated equations

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. © 2005 - IOS Press and the authors. All rights reserved.