Boundedness in a two-dimensional attraction-repulsion system with nonlinear diffusion

This paper is devoted to the attraction-repulsion chemotaxis system with nonlinear diffusion: (u(t) =del .(D(u)del u)- chi del . (u del v) + zeta del.(u del w)+uf(u), x epsilon Omega, t >0, v(t) = Delta(v) - alpha(1)v + beta(1)u, x is an element of Omega, t > 0, w(t) = Delta(w) - alpha(2)w +beta(2)u, x is an element of Omega t > 0, where > 0, > 0, (i)>0, (i)>0 (i = 1,2) and f(s) - s. In two-space dimension, we prove the global existence and uniform boundedness of the classical solution to this model for any > 0. Copyright (c) 2015 John Wiley & Sons, Ltd.