Nonlocal anisotropic dispersal with monostable nonlinearity
Jerome Coville (BIOSP), Juan Davila (CMM, DIM), Salome Martinez (CMM,, DIM)
TL;DR
This paper investigates traveling wave solutions in a nonlocal anisotropic dispersal model with monostable nonlinearity, establishing existence, minimal speed, and conditions for uniqueness or nonuniqueness of solutions.
Contribution
It introduces new results on existence and uniqueness of traveling wave profiles in nonlocal anisotropic dispersal equations with monostable nonlinearities.
Findings
Existence of a minimal wave speed c for the traveling wave solutions.
Uniqueness of the wave profile at c=0 under certain conditions.
Examples demonstrating nonuniqueness of solutions at c=0.
Abstract
We study the travelling wave problem J\astu - u - cu' + f (u) = 0 in R, u(-\infty) = 0, u(+\infty) = 1 with an asymmetric kernel J and a monostable nonlinearity. We prove the existence of a minimal speed, and under certain hypothesis the uniqueness of the profile for c = 0. For c = 0 we show examples of nonuniqueness.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.