Spatial dynamics for a model of epidermal wound healing

  • 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

    Related Papers:

  • 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.


    加载中
    [1] in Partial Differential Equations and Related Topics (ed. J. A. Goldstein), Lecture Notes in Mathematics Ser., 446, Springer-Verlag, Berlin, 1975, 5-49.
    [2] Adv. Math., 30 (1978), 33-76.
    [3] Math. Biosci., 124 (1994), 127-147.
    [4] J. Dynam. Differential Equations, 14 (2002), 85-137.
    [5] Phys. D, 165 (2002), 176-198.
    [6] Ann. of Eugenics, 7 (1937), 355-369.
    [7] Discrete Contin. Dyn. Syst., 12 (2005), 193-212.
    [8] Comm. Pure Appl. Math., 52 (1999), 1255-1276.
    [9] Cambridge University Press, Cambridge, 1985.
    [10] SIAM J. Math. Anal., 40 (2008), 776-789.
    [11] Bull. Moscow Univ. Math. Mech., 1 (1937), 1-26.
    [12] Commun. Pure Appl. Math., 60 (2007), 1-40.
    [13] J. Math. Pures Appl., 90 (2008), 492-504.
    [14] J. Math. Biol., 45 (2002), 219-233.
    [15] Math. Biosci., 196 (2005), 82-98.
    [16] J. Math. Biol., 58 (2009), 323-338.
    [17] Math. Biosci., 93 (1989), 269-295.
    [18] Springer-Verlag, New York, 2003.
    [19] J. Differential Equations, 237 (2007), 259-277.
    [20] SIAM J. Math. Anal., 40 (2009), 2217-2240.
    [21] Springer-Verlag, New York, 1984.
    [22] Proc. R. Soc. London B, 241 (1990), 29-36.
    [23] J. Math. Biol., 29 (1991), 389-404.
    [24] Springer-Verlag, New York, 1994.
    [25] J. Math. Biol., 8 (1979), 173-187.
    [26] J. Differential Equations, 247 (2009), 887-905.
    [27] Discrete and Continuous Dynamical Systems B, 17 (2012), 2243-2266.
    [28] J. Nonlinear Sci., 21 (2011), 747-783.
    [29] Nonlinearity, 23 (2010), 1609-1630.
    [30] Trans. Amer. Math. Soc., 361 (2009), 2047-2084.
    [31] J. Math. Biol., 45 (2002), 183-218.
    [32] in Nonlinear Partial Differential Equations and Applications (ed. J. M. Chadam), Lecture Notes in Mathematics, 648, Springer-Verlag, Berlin, 1978, 47-96.
    [33] Discrete Contin. Dyn. Syst., 23 (2009), 1087-1098.
    [34] Nonlinearity, 25 (2012), 2785-2801.
    [35] J. Dynam. Diff. Eqns., 25 (2013), 505-533.
    [36] Discrete Contin. Dyn. Syst., 33 (2013), 921-946.
    [37] Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 883-904.
    [38] J. Math. Anal. Appl., 401 (2013), 85-97.
    [39] Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 2164-2176.
  • Reader Comments
  • © 2014 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2047) PDF downloads(473) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog