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Indexed by:期刊论文

Date of Publication:2015-04-01

Journal:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:116

Page Number:1-18

ISSN No.:0362-546X

Key Words:Keller-Segel model; Degenerate diffusion; Nonlocal aggregation; Global existence; Blow-up

Abstract:In this paper, we study the degenerate Keller-Segel equation with nonlocal aggregation u(t) = Delta u(m) -del. (uB(u)) in R-d x R+, where m > 1, d >= 3, and B(u) = Delta((-del)(-beta/2) u) with beta is an element of [ 2, d). By analyzing the interaction between the degenerate diffusion and the nonlocal aggregation, we determine the conditions for initial data under which weak solutions globally exist or blow up in finite time with m is an element of (1, d+v/d) .v = d - beta sharper criterion is given for global existence and finite time blow-up of weak solutions with m in the subrange (2d/2d-v, d broken vertical bar v/d) subset of (1, d broken vertical bar v/d) d). (C) 2014 Elsevier Ltd. All rights reserved.