# American Institute of Mathematical Sciences

2015, 2015(special): 1125-1133. doi: 10.3934/proc.2015.1125

## Existence of solutions to chemotaxis dynamics with logistic source

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

Received  July 2014 Revised  November 2014 Published  November 2015

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].
Citation: Tomomi Yokota, Noriaki Yoshino. Existence of solutions to chemotaxis dynamics with logistic source. Conference Publications, 2015, 2015 (special) : 1125-1133. doi: 10.3934/proc.2015.1125
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