
Infinite time blow-up in the Keller-Segel system: existence and stability
Davila, Juan; Del Pino, Manuel; Dolbeault, Jean; Musso, Monica; Wei, Juncheng (2019), Infinite time blow-up in the Keller-Segel system: existence and stability. https://basepub.dauphine.fr/handle/123456789/20449
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Type
Document de travail / Working paperExternal document link
https://hal.archives-ouvertes.fr/hal-02394787Date
2019Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-DauphinePublished in
Paris
Pages
22
Metadata
Show full item recordAuthor(s)
Davila, JuanDepartment of Mathematical Sciences, University of Bath
Del Pino, Manuel
Department of Mathematical Sciences, University of Bath
Dolbeault, Jean

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Musso, Monica
Department of Mathematical Sciences, University of Bath
Wei, Juncheng
University of British Columbia
Abstract (EN)
The simplest version of the parabolic-elliptic Patlak-Keller-Segel system in the two-dimensional Euclidean space has an 8π critical mass which corresponds to the exact threshold between finite-time blow-up and self-similar diffusion towards zero. Among functions with mass 8π, we find a neighborhood of a radial function such that any solution with initial condition in this neighborhood is globally defined and blows-up in infinite time with an explicit scaling involving the square root of the logarithm of the time.Subjects / Keywords
Patlak-Keller-Segel system; chemotaxis; critical mass; blow-up; infinite time blow-up; inner-outer gluing scheme; rate; blow-up profileRelated items
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