Existence of traveling wave solutions for density-dependent diffusion competitive systems. (English) Zbl 07900886
This paper considers the existence of traveling wave solutions for two species competitive systems with density-dependent diffusion. Since the density-dependent diffusion is a kind of nonlinear diffusion and degenerates at the origin, the methods for proving the existence of traveling wave solutions for competitive systems with linear diffusion are invalid. To overcome the degeneracy of diffusion, we construct a nonlinear invariant region near the origin. By using the method of phase plane analysis, we prove the existence of traveling wave solutions. The existence of the minimal speed is given and the information of traveling waves is given.
Reviewer: Yu Ichida (Sanda)
MSC:
| 35C07 | Traveling wave solutions |
| 35K40 | Second-order parabolic systems |
| 35K65 | Degenerate parabolic equations |
| 92D25 | Population dynamics (general) |
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