Spreading speeds and traveling waves for a model of epidermal wound healing

In this paper, we shall establish the spreading speed and existence of traveling waves for a non-cooperative system arising from epidermal wound healing and characterize the spreading speed as the slowest speed of a family of non-constant traveling wave solutions. Our results on the spreading speed and traveling waves can also be applied to a large class of non-cooperative reaction-diffusion systems.

💡 Research Summary

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The paper addresses a two‑component reaction‑diffusion system that models epidermal wound healing, where one component represents the density of keratinocytes and the other the concentration of a growth factor. Unlike many classical models, the interaction terms are of opposite sign, rendering the system non‑cooperative. This non‑cooperativity prevents the direct use of standard monotone‑iteration and comparison‑principle techniques that are available for cooperative (monotone) systems.

The authors first linearize the system around the trivial steady state (zero cell density and zero growth factor) and study the associated eigenvalue problem
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