Long‐time asymptotics via entropy methods for diffusion dominated equations

Article type: Research Article

Authors: Carrillo, José A.^; | Fellner, Klemens

Affiliations: ICREA, Departament de Matemàtiques, Universitat Autònoma de Barcelona, E‐08193, Bellaterra, Spain | Faculty of Mathematics, University of Vienna, Nordbergstraße 15, A‐1090 Vienna, Austria

Note: [] Corresponding author. E‐mail: carrillo@mat.uab.es.

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.

Keywords: convection–diffusion, absorption–diffusion, entropy methods, large time behaviour, convergence rate

Journal: Asymptotic Analysis, vol. 42, no. 1-2, pp. 29-54, 2005