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Mathematical Biosciences and Engineering

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

  • 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: 01 April 2013 Accepted: 29 June 2018 Published: 01 June 2014

  • MSC : 35K57, 92C50.

  • 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 speedof 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.

    Citation: Haiyan Wang, Shiliang Wu. Spatial dynamics for a model of epidermal wound healing[J]. Mathematical Biosciences and Engineering, 2014, 11(5): 1215-1227. doi: 10.3934/mbe.2014.11.1215

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  • 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 speedof 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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