A simple approach to the wave uniqueness problem
arXiv:1808.04857 · doi:10.1016/j.jde.2018.11.012
Abstract
We propose a new approach for proving uniqueness of semi-wavefronts in generally non-monotone monostable reaction-diffusion equations with distributed delay. This allows to solve an open problem concerning the uniqueness of non-monotone (hence, slowly oscillating) semi-wavefronts to the KPP-Fisher equation with delay. Similarly, a broad family of the Mackey-Glass type diffusive equations is shown to possess a unique (up to translation) semi-wavefront for each admissible speed.
arXiv comment12 pages, submitted
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- Nonstandard quasi-monotonicity: an application to the wave existence in a neutral KPP-Fisher equation
- Existence and uniqueness of monotone wavefronts in a nonlocal resource-limited model
- On the geometric diversity of wavefronts for the scalar Kolmogorov ecological equation