Asymptotic Behavior of Solution to Some Models Involving Two Species All with Chemotaxis (Journal of Partial Differential Equations, 2009)
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.
Keywords: Chemotaxis model; asymptotical behavior of solution; blow-up; quenching; comparison