Year: 2009
Journal of Partial Differential Equations, Vol. 22 (2009), Iss. 3 : pp. 266–281
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v22.n3.5
Journal of Partial Differential Equations, Vol. 22 (2009), Iss. 3 : pp. 266–281
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Chemotaxis model