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Existence and asymptotic behaviour for the time‐fractional Keller–Segel model for chemotaxis
Author(s) -
Azevedo Joelma,
Cuevas Claudio,
Henriquez Erwin
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700237
Subject(s) - mathematics , class (philosophy) , order (exchange) , chemotaxis , pure mathematics , mathematical analysis , computer science , economics , artificial intelligence , biochemistry , chemistry , receptor , finance
One of the most important systems for understanding chemotactic aggregation is the Keller–Segel system. We consider the time‐fractional Keller–Segel system of order α ∈ ( 0 , 1 ) . We prove an existence result with small initial data in a class of Besov–Morrey spaces. Self‐similar solutions are obtained and we also show an asymptotic behaviour result.