Global existence of solutions to the Cauchy problem for an attraction repulsion chemotaxis system in R-2 in the attractive dominant case

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.