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.
Highlights
In this paper, we study the spatial dynamics, including spreading speeds, traveling wave solutions and entire solutions of a non-cooperative reaction-diffusion systems arising from wound healing
Traveling wave solutions and spreading speeds for reaction-diffusion equations have been studied by a number of researchers
The following theorem on traveling wave solutions and spreading speed for general non-cooperative systems is from [28]
Summary
We study the spatial dynamics, including spreading speeds, traveling wave solutions and entire solutions of a non-cooperative reaction-diffusion systems arising from wound healing. Traveling waves, spreading speed, entire solution, non-cooperative diffusion systems, epidermal wound healing. Traveling wave solutions and spreading speeds for reaction-diffusion equations have been studied by a number of researchers. In a recent paper [28], one of the authors studied traveling waves and spreading speeds of propagation for a class of non-cooperative reaction-diffusion systems and the model discussed in [33]. The following theorem on traveling wave solutions and spreading speed for general non-cooperative systems is from [28]. The linearization of (1.1) at the origin is d1∆u1 + (1 − 2κ)u1
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