Boundedness in a two‐dimensional attraction–repulsion system with nonlinear diffusion

Abstract

This paper is devoted to the attraction–repulsion chemotaxis system with nonlinear diffusion: urn:x-wiley:mma:media:mma3477:mma3477-math-0001 where χ > 0, ζ > 0, α i >0, β i >0 ( i = 1,2) and f ( s )≤ κ − μ s τ . In two‐space dimension, we prove the global existence and uniform boundedness of the classical solution to this model for any μ > 0. Copyright © 2015 John Wiley & Sons, Ltd.