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Abstract:

We extend the existing theory on large-time asymptotics for convection-diffusion equations, based on the entropy-entropy dissipation approach, to certain fast diffusion equations with uniformly convex confinement potential and finite-mass but infinite-entropy equilibrium solutions. We prove existence of a mass preserving solution of the Cauchy problem and we show exponential convergence, as t → ∞, at a precise rate to the corresponding equilibrium solution in the L1 norm. As by-product we also derive corresponding generalized Sobolev inequalities.

Registro:

Documento: Artículo
Título:On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass
Autor:Lederman, C.; Markowich, P.A.
Filiación:Departamento de Matematica, Facultad de Ciencias Exactas, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Institut für Mathematik, Universität Wien, Vienna, Austria
Año:2003
Volumen:28
Número:1-2
Página de inicio:301
Página de fin:332
DOI: http://dx.doi.org/10.1081/PDE-120019384
Título revista:Communications in Partial Differential Equations
Título revista abreviado:Commun. Partial Differ. Equ.
ISSN:03605302
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v28_n1-2_p301_Lederman

Referencias:

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Citas:

---------- APA ----------
Lederman, C. & Markowich, P.A. (2003) . On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass. Communications in Partial Differential Equations, 28(1-2), 301-332.
http://dx.doi.org/10.1081/PDE-120019384
---------- CHICAGO ----------
Lederman, C., Markowich, P.A. "On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass" . Communications in Partial Differential Equations 28, no. 1-2 (2003) : 301-332.
http://dx.doi.org/10.1081/PDE-120019384
---------- MLA ----------
Lederman, C., Markowich, P.A. "On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass" . Communications in Partial Differential Equations, vol. 28, no. 1-2, 2003, pp. 301-332.
http://dx.doi.org/10.1081/PDE-120019384
---------- VANCOUVER ----------
Lederman, C., Markowich, P.A. On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass. Commun. Partial Differ. Equ. 2003;28(1-2):301-332.
http://dx.doi.org/10.1081/PDE-120019384