Abstract
We construct nontrivial entire solutions for a bistable reaction–diffusion equation in a class of domains that are unbounded in one direction. The motivation comes from recent results of Berestycki et al. (Calc Var Partial Differ Equ 55(3):1–32, 2016) concerning propagation and blocking phenomena in infinite domains. A key assumption in their study was the “cylinder-like” assumption: their domains are supposed to be straight cylinders in a half space. The purpose of this paper is to consider domains that tend to a straight cylinder in one direction. We need a different approach based on the long time stability of the bistable wave in heterogeneous media. We also prove the existence of an entire solution for a one-dimensional problem with a non-homogeneous linear term.
Original language | English (US) |
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Pages (from-to) | 1273-1293 |
Number of pages | 21 |
Journal | Journal of Dynamics and Differential Equations |
Volume | 30 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1 2018 |
Bibliographical note
Publisher Copyright:© 2017, Springer Science+Business Media, LLC.
Keywords
- Bistable equations
- Invasion fronts
- Reaction-diffusion equations