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Indexed by:期刊论文

Date of Publication:2016-03-01

Journal:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals:SCIE、EI

Volume:134

Page Number:204-214

ISSN No.:0362-546X

Key Words:Keller-Segel model; Degenerate diffusion; Nonlocal aggregation; Uniqueness of weak solutions; Optimal transportation; Wasserstein distance

Abstract:This paper considers weak solutions to the degenerate Keller-Segel equation with nonlocal aggregation: u(t) = Delta u(m) - del . (uB(u)) in R-d x R+, where B(u) = del((-Delta)(-beta/2) u), d >= 3, beta is an element of [2, d), 1 < m < 2 - beta/d. In a previous paper of the authors (Hong et al., 2015), a criterion was established for global existence versus finite time blow-up of weak solutions to the problem. A natural question is whether the uniqueness is true for the weak solutions obtained. A positive answer is given in this paper that the global weak solutions must be unique provided the second moment of initial data is finite, which means that the weak solutions are weak entropy solutions in fact. The framework of the proof is based on the optimal transportation method. (C) 2016 Elsevier Ltd. All rights reserved.