Existence of  solutions to chemotaxis dynamics           with logistic source

Tomomi  Yokota; Noriaki  Yoshino

doi:10.3934/proc.2015.1125

Article Contents

2015, Volume 2015: 1125-1133. Doi: 10.3934/proc.2015.1125 open access

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Existence of solutions to chemotaxis dynamics with logistic source

Tomomi Yokota^1, and
Noriaki Yoshino^1,

1.
Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601

Received: July 2014

Revised: November 2014

Published: October 2015

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Abstract

This paper is concerned with a chemotaxis system with nonlinear diffusion and logistic growth term $f(b) = \kappa b-\mu |b|^{\alpha-1}b$ with $\kappa>0$, $\mu>0$ and $\alpha > 1$ under the no-flux boundary condition. It is shown that there exists a local solution to this system for any $L^2$-initial data and that under a stronger assumption on the chemotactic sensitivity there exists a global solution for any $L^2$-initial data. The proof is based on the method built by Marinoschi [8].

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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