Traveling bands for the Keller-Segel model with population growth

Shangbing Ai; Zhian Wang

doi:10.3934/mbe.2015.12.717

Article Contents

2015, Volume 12, Issue 4: 717-737. Doi: 10.3934/mbe.2015.12.717 open access

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Traveling bands for the Keller-Segel model with population growth

Shangbing Ai^1, and
Zhian Wang²

1.
Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899
2.
Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong

Received: March 31, 2014

Revised: October 31, 2014

Published: March 2015

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Abstract

This paper is concerned with the existence of the traveling bands to the Keller-Segel model with cell population growth in the form of a chemical uptake kinetics. We find that when the cell growth is considered, the profile of traveling bands, the minimum wave speed and the range of the chemical consumption rate for the existence of traveling wave solutions will change. Our results reveal that collective interaction of cell growth and chemical consumption rate plays an essential role in the generation of traveling bands. The research in the paper provides new insights into the mechanisms underlying the chemotactic pattern formation of wave bands.

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Mathematics Subject Classification: 35C07, 35K55, 46N60, 62P10, 92C17.

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