Traveling waves for time-delayed reaction diffusion equations with degenerate diffusion. (English) Zbl 1406.35087
This paper is concerned with a reaction-diffusion equation with degenerate diffusion, including a time delayed and spatially nonlocal term. This arises from a simplification of an age structured population model where, typically, immature individuals disperse faster than mature individuals. The authors first show that this equation admits some traveling wave solutions. The main goal of this paper is then to show that the minimal traveling wave speed goes to zero as a diffusion parameter goes to zero if and only if the equation is truly nonlocal. This suggests that the whole population still spreads even if only the immature population is motile.
Reviewer: Thomas Giletti (Vandœuvre-lès-Nancy)
MSC:
| 35C07 | Traveling wave solutions |
| 35K57 | Reaction-diffusion equations |
| 35R09 | Integro-partial differential equations |
| 35K65 | Degenerate parabolic equations |
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