一种圆形表皮伤口愈合模型整体解的存在唯一性

Existence and Uniqueness of Global Solutions of a Mathematical Model for the Healing of a Circular Epidermal Wound

提出一种一般化了的圆形表皮伤口愈合数学模型。在该模型中,伤口愈合受到表皮细胞密度和化学物质浓度的共同影响。利用抛物型方程的理论和Banach不动点定理证明了该问题局部解的存在唯一性。在此基础上,利用延拓方法证明了整体解的存在唯一性.

In this paper,a generalized mathematical model for the healing of circular epidermal wounds is proposed based on other papers.The healing process in the model is regulated by epidermal cell density and chemical concentration.With the theory of parabolic equations and the Banach fixed point theorem the author proves the existence and uniqueness of a local solution,and then acquires the existence and uniqueness of the global solution by the continuation method.