This paper is concerned with the asymptotic behavior of solution to the following model involving two species all with chemotaxis: \frac{∂p}{∂t}=D_p∇(p∇ln\frac{p}{ω}), \frac{∂q}{∂t}=D_q∇(q∇ln\frac{q}{ω}), \frac{∂ω}{∂t}=βp-δω, p∇ln(\frac{p}{ω}·\vec{n}=q∇ln\frac{q}{ω})·\vec{n}=0. We prove that the solution exists globally as β ≥ 0. As β < 0, whether the solution exists globally or not depends on the initial data. By function transformation and comparison, the asymptotical behavior of the solution is studied.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v22.n3.5}, url = {http://global-sci.org/intro/article_detail/jpde/5257.html} }