Global existence of solutions to the Cauchy problem for an attraction repulsion chemotaxis system in R2 in the attractive dominant case

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Nagai, Toshitaka¹  Yamada, Tetsuya² 

[1] Hiroshima Univ, Dept Math, Higashihiroshima 7398526, Japan

[2] Pukui Coll, Natl Inst Technol, Course Gen Educ Sci, Sabae, Fukui 9168507, Japan

关键词: Attraction-repulsion chemotaxis system;    A priori estimate;    Global existence;   

DOI  :  10.1016/j.jmaa.2018.02.057

来源: Elsevier

【 摘 要 】

We consider the Cauchy problem for an attraction repulsion chemotaxis system in R-2 with the chemotactic coefficient of the attractant beta(1) and that of the repellent beta(2). It is known that in the repulsive dominant case beta(1) < beta(2) or the balance case beta(1)= beta(2), the nonnegative solutions to the Cauchy problem exist globally in time, whereas in the attractive dominant case beta(1) < beta(2), there are blowing -up solutions in finite time under the assumption (beta(1) - beta(2))integral(R2) u(0) dx > 8 pi on the nonnegative initial data uo. In this paper, we show the global existence of nonnegative solutions to the Cauchy problem under the assumption (beta(1) - beta(2)) integral(R2) u(0) dx < 8 pi in the attractive dominant case. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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