期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 258, 期 4, 页码 1158-1191出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2014.10.016
关键词
Chemotaxis; Logistic source; Existence; Weak solutions; Eventual smoothness
类别
We prove existence of global weak solutions to the chemotaxis system u(t) = Delta u - del . (u del v) + kappa u - mu u(2) v(t) = Delta v - v + u under homogeneous Neumann boundary conditions in a smooth bounded convex domain Omega subset of R-n, for arbitrarily small values of mu > 0. Additionally, we show that in the three-dimensional setting, after some time, these solutions become classical solutions, provided that kappa is not too large. In this case, we also consider their large-time behaviour: We prove decay if kappa <= 0 and the existence of an absorbing set if kappa > 0 is sufficiently small. (C) 2014 Elsevier Inc. All rights reserved.
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