2026-04-03T23:16:38Zhttps://recercat.cat/oai/request

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

Semidiscretization and long-time asymptotics of nonlinear diffusion equations Carrillo de la Plata, José Antonio di Francesco, Marco Gualdani, Maria P. Centre de Recerca Matemàtica Burger, Equacions de Desenvolupaments asimptòtics 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. 2005 Article Prepublicació https://ddd.uab.cat/record/44162 urn:oai:ddd.uab.cat:44162 eng Centre de Recerca Matemàtica. Prepublicacions ; open access Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. https://creativecommons.org/licenses/by-nc-nd/2.5/ application/pdf Centre de Recerca Matemàtica,