Classical solutions for a logarithmic fractional diffusion equation

Rodríguez Santa María, Ana and Pablo, Arturo de and Quirós, Fernando and Vázquez, Juan Luis (2014). Classical solutions for a logarithmic fractional diffusion equation. "Journal de Mathematiques Pures Et Appliquees", v. 101 (n. 6); pp. 901-924. ISSN 0021-7824. https://doi.org/10.1016/j.matpur.2013.10.009.

Description

Title: Classical solutions for a logarithmic fractional diffusion equation
Author/s:
  • Rodríguez Santa María, Ana
  • Pablo, Arturo de
  • Quirós, Fernando
  • Vázquez, Juan Luis
Item Type: Article
Título de Revista/Publicación: Journal de Mathematiques Pures Et Appliquees
Date: June 2014
ISSN: 0021-7824
Volume: 101
Subjects:
Faculty: E.T.S. Arquitectura (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2011-24696UnspecifiedUnspecifiedUnspecified
Government of SpainMTM2011-25287UnspecifiedUnspecifiedUnspecified

More information

Item ID: 40259
DC Identifier: http://oa.upm.es/40259/
OAI Identifier: oai:oa.upm.es:40259
DOI: 10.1016/j.matpur.2013.10.009
Official URL: arXiv:1205.2223v2
Deposited by: Memoria Investigacion
Deposited on: 06 May 2016 10:46
Last Modified: 12 Jun 2019 11:37
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