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

Junfeng Li & Weian Liu

DOI: 10.4208/jpde.v22.n3.5

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

Published online: 2009-08

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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.

  • Keywords

Chemotaxis model asymptotical behavior of solution blow-up quenching comparison

  • AMS Subject Headings

35K57 35M20 92D25 35Q80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-22-266, author = {Junfeng Li and Weian Liu }, title = {Asymptotic Behavior of Solution to Some Models Involving Two Species All with Chemotaxis}, journal = {Journal of Partial Differential Equations}, year = {2009}, volume = {22}, number = {3}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v22.n3.5}, url = {http://global-sci.org/intro/article_detail/jpde/5257.html} }
TY - JOUR T1 - Asymptotic Behavior of Solution to Some Models Involving Two Species All with Chemotaxis AU - Junfeng Li & Weian Liu JO - Journal of Partial Differential Equations VL - 3 SP - 266 EP - 281 PY - 2009 DA - 2009/08 SN - 22 DO - http://doi.org/10.4208/jpde.v22.n3.5 UR - https://global-sci.org/intro/article_detail/jpde/5257.html KW - Chemotaxis model KW - asymptotical behavior of solution KW - blow-up KW - quenching KW - comparison AB -

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.

Junfeng Li and Weian Liu . (2009). Asymptotic Behavior of Solution to Some Models Involving Two Species All with Chemotaxis. Journal of Partial Differential Equations. 22 (3). 266-281. doi:10.4208/jpde.v22.n3.5
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