2026-04-19T12:49:41Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4525312026-02-11T09:11:49Zcom_2072_98col_2072_378195

00925njm 22002777a 4500 dc Carrillo de la Plata, José Antonio author di Francesco, Marco author Gualdani, Maria P. author Centre de Recerca Matemàtica author 2005 We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero. Burger, Equacions de Desenvolupaments asimptòtics Semidiscretization and long-time asymptotics of nonlinear diffusion equations