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Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations

Abstract: In this paper we consider a dd-dimensional (d=1,2d=1,2) parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order ??(0,2)??(0,2). We prove uniform in time boundedness of its solution in the supercritical range ?>d(1?c)?>d(1?c), where cc is an explicit constant depending on parameters of our problem. Furthermore, we establish sufficient conditions for ?u(t)?u??L??0?u(t)?u??L??0, where u??1u??1 is the only nontrivial homogeneous solution. Finally, we provide a uniqueness result.

 Fuente: Discrete and continuous dynamical systems series S Volume 13, Number 2, April 2020

Editorial: American Institute of Mathematical Sciences

 Fecha de publicación: 01/04/2020

Nº de páginas: 26

Tipo de publicación: Artículo de Revista

 DOI: 10.3934/dcdss.2020008

ISSN: 1937-1632,1937-1179

Proyecto español: MTM2014-59488-P

Url de la publicación: https://doi.org/10.3934/dcdss.2020008

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