Regular traveling waves for a nonlocal diffusion equation
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.
nonlocal diffusion equations, delayed nonlinearity
scientific article; zbMATH DE number 6361739
scientific article