Wavefront of an angiogenesis model

Zhi-An Wang

doi:10.3934/dcdsb.2012.17.2849

Article Contents

2012, Volume 17, Issue 8: 2849-2860. Doi: 10.3934/dcdsb.2012.17.2849

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Wavefront of an angiogenesis model

Zhi-An Wang^1,

1.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received: February 28, 2011

Revised: May 31, 2011

Published: October 2012

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Abstract

In this paper, we show the existence of traveling wave solutions to a chemotaxis model describing the initiation of angiogenesis. By a change of dependent variable, we transform the wave equation of the angiogenesis model to a Fisher type wave equation. Then we make use of the methods of analyzing the Fisher wave equation to obtain the existence of traveling wave solutions to the angiogenesis model. In virtue of the asymptotic behavior of the traveling wave solution at infinity, we find the explicit wave speed for cases of both zero and nonzero chemical diffusion. Finally based on the fact that the wave speed is convergent with respect to the chemical diffusion, we rigorously establish the zero chemical diffusion limit of traveling wave solutions by the energy estimates.

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

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