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Abstract:

In this paper we investigate the large-time asymptotic of linearized very fast diffusion equations with and without potential confinements. These equations do not satisfy, in general, logarithmic Sobolev inequalities, but, as we show by using the 'Bakry-Emery reverse approach', in the confined case they have a positive spectral gap at the eigenvalue zero. We present estimates for this spectral gap and draw conclusions on the time decay of the solution, which we show to be exponential for the problem with confinement and algebraic for the pure diffusive case. These results hold for arbitrary algebraically large diffusion speeds, if the solutions have the mass-conservation property.

Registro:

Documento: Artículo
Título:Poincaré inequalities for linearizations of very fast diffusion equations
Autor:Carrillo, J.A.; Lederman, C.; Markowich, P.A.; Toscani, G.
Filiación:Depto. de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
Departamento de Matemática, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Institüt für Mathematik, Universität Wien, Boltzmanngasse 9, A-1090 Wien, Austria
Dipartimento di Matematica, Universitá di Pavia, Via Ferrata 1, 27100 Pavia, Italy
Año:2002
Volumen:15
Número:3
Página de inicio:565
Página de fin:580
DOI: http://dx.doi.org/10.1088/0951-7715/15/3/303
Título revista:Nonlinearity
Título revista abreviado:Nonlinearity
ISSN:09517715
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09517715_v15_n3_p565_Carrillo

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Citas:

---------- APA ----------
Carrillo, J.A., Lederman, C., Markowich, P.A. & Toscani, G. (2002) . Poincaré inequalities for linearizations of very fast diffusion equations. Nonlinearity, 15(3), 565-580.
http://dx.doi.org/10.1088/0951-7715/15/3/303
---------- CHICAGO ----------
Carrillo, J.A., Lederman, C., Markowich, P.A., Toscani, G. "Poincaré inequalities for linearizations of very fast diffusion equations" . Nonlinearity 15, no. 3 (2002) : 565-580.
http://dx.doi.org/10.1088/0951-7715/15/3/303
---------- MLA ----------
Carrillo, J.A., Lederman, C., Markowich, P.A., Toscani, G. "Poincaré inequalities for linearizations of very fast diffusion equations" . Nonlinearity, vol. 15, no. 3, 2002, pp. 565-580.
http://dx.doi.org/10.1088/0951-7715/15/3/303
---------- VANCOUVER ----------
Carrillo, J.A., Lederman, C., Markowich, P.A., Toscani, G. Poincaré inequalities for linearizations of very fast diffusion equations. Nonlinearity. 2002;15(3):565-580.
http://dx.doi.org/10.1088/0951-7715/15/3/303