Volume 22, Issue 3
Asymptotic Behavior of Solution to Some Models Involving Two Species All with Chemotaxis

Junfeng Li and Weian Liu

10.4208/jpde.v22.n3.5

J. Part. Diff. Eq., 22 (2009), pp. 266-281.

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  • Abstract

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.

  • History

Published online: 2009-08

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