Spatial dynamics for a model of epidermal wound healing

Haiyan Wang; Shiliang Wu

doi:10.3934/mbe.2014.11.1215

Article Contents

2014, Volume 11, Issue 5: 1215-1227. Doi: 10.3934/mbe.2014.11.1215

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Spatial dynamics for a model of epidermal wound healing

Haiyan Wang^1, and
Shiliang Wu^2,

1.
Division of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069-7100
2.
School of Mathematics and Statistics, Xidian University, Xi’an, Shaanxi 710071

Received: March 31, 2013

Revised: January 31, 2014

Published: May 2014

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Abstract

In this paper, we consider the spatial dynamics for a non-cooperative diffusion system arising from epidermal wound healing. We shall establish the spreading speed and existence of traveling waves and characterize the spreading speed as the slowest speed of a family of non-constant traveling wave solutions. We also construct some new types of entire solutions which are different from the traveling wave solutions and spatial variable independent solutions. The traveling wave solutions provide the healing speed and describe how wound healing process spreads from one side of the wound. The entire solution exhibits the interaction of several waves originated from different locations of the wound. To the best of knowledge of the authors, it is the first time that it is shown that there is an entire solution in the model for epidermal wound healing.

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Mathematics Subject Classification: 35K57, 92C50.

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