Competitive exclusion in a two-species chemotaxis model (Q2249666)

The aim of this work is to study the existence and stability of a certain competitive model between two-species chemotaxis. The model is given by a system of reaction diffusion equations of two species. First, the authors study the local existence and global continuations of the solutions, some results are provided about the boundedness and the maximal interval where the solution exists. Then authors study also the long-time behavior of the solutions. From that study, the authors provide parameter regimes for which one of the species dies asymptotically while the other does not.