Regular traveling waves for a nonlocal diffusion equation. (English) Zbl 1323.35089
In this paper, the authors study a nonlocal diffusion equation with a general diffusion kernel and delayed non-linearity, and obtain the existence, nonexistence and uniqueness of the regular traveling wave solutions for this nonlocal diffusion equation. The existence of traveling wave solutions is proved by upper-lower solutions (large wave speed) and passing to a limit function (minimal wave speed). For both monotone and non-monotone cases, the uniqueness up to transition is investigated. As an application of the results, the authors reconsider some models arising from population dynamics, epidemiology and neural networks.
Reviewer: Guo Lin (Lanzhou)
MSC:
| 35K57 | Reaction-diffusion equations |
| 92D25 | Population dynamics (general) |
| 45G10 | Other nonlinear integral equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35C07 | Traveling wave solutions |
| 35R09 | Integro-partial differential equations |
Keywords:
regular traveling waves; existence and uniqueness; nonlocal diffusion equations, delayed nonlinearityReferences:
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