GLOBAL WEAK SOLUTIONS OF A PARABOLIC-ELLIPTIC KELLER-SEGEL SYSTEM WITH GRADIENT DEPENDENT CHEMOTACTIC COEFFICIENTS
Source
Discrete and Continuous Dynamical Systems - Series B
Author(s)
Abstract
We consider the following Keller-Segel system with gradient dependent chemotactic coefficient: {u<inf>t</inf> = ?u ? ?? � (uf(|?v|)?v), 0 = ?v ? v + g(u), in smooth bounded domains ? ? Rn, n ? 1 with f(?) = (?p?2(1+?p)q? p/p), 1 < q ? p < ? and g(?) = ?/(1+?<inf>)</inf>1-?, ? ? 0, ? ? [0, 1]. We show the existence of a global weak solution, bounded in L?-norm, if 1 < q ? p {< ?, n = 1, 1 < q < <inf>n?</inf>n<inf>1</inf> , n ? 2. � 2023 Elsevier B.V., All rights reserved.