# American Institute of Mathematical Sciences

December  2007, 6(4): 1145-1165. doi: 10.3934/cpaa.2007.6.1145

## Finite traveling wave solutions in a degenerate cross-diffusion model for bacterial colony

 1 Department of Physical Sciences and Mathematics, Florida Gulf Coast University, Fort Myers, FL 33965-6565, United States 2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States

Received  January 2007 Revised  May 2007 Published  September 2007

In this paper we study the existence of finite traveling wave solutions in a degenerate cross-diffusion system modeling the growth of bacteria colony. The importance of establishing the existence lies in the fact that the analysis of the stability of the wave front provides partial answers to the intriguing spatial patterns of the colony. There have been very few results on the finite traveling wave solutions of degenerate parabolic system. One reason is that the traditional method often leads to phase plane analysis on higher dimension which is usually a difficult task. Our method in this paper is based on Schauder fixed point theorem and shooting arguments.
Citation: Peng Feng, Zhengfang Zhou. Finite traveling wave solutions in a degenerate cross-diffusion model for bacterial colony. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1145-1165. doi: 10.3934/cpaa.2007.6.1145
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