Entire solutions of monotone bistable reaction–diffusion systems in RN

Wei Jie Sheng; Zhi Cheng Wang

doi:10.1007/s00526-018-1437-4

Entire solutions of monotone bistable reaction–diffusion systems in R^N

Wei Jie Sheng^*
, Zhi Cheng Wang

^*Corresponding author for this work

School of Mathematics

Institut de Mathématiques de Marseille
Lanzhou University

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

This paper is concerned with entire solutions of monotone bistable reaction–diffusion systems in R^N. We first show that there is a new entire solution for bistable reaction–diffusion systems which behaves as three moving planar fronts as time goes to -∞ and as a V-shaped traveling front as time goes to ∞. Then we address the speed of the interfaces corresponding to the entire solution by appealing to the super-sub solutions technique. Finally, we apply our results to two important models in biology.

Original language	English
Article number	145
Journal	Calculus of Variations and Partial Differential Equations
Volume	57
Issue number	6
DOIs	https://doi.org/10.1007/s00526-018-1437-4
State	Published - 1 Dec 2018

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abstract = "This paper is concerned with entire solutions of monotone bistable reaction–diffusion systems in RN. We first show that there is a new entire solution for bistable reaction–diffusion systems which behaves as three moving planar fronts as time goes to -∞ and as a V-shaped traveling front as time goes to ∞. Then we address the speed of the interfaces corresponding to the entire solution by appealing to the super-sub solutions technique. Finally, we apply our results to two important models in biology.",

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AB - This paper is concerned with entire solutions of monotone bistable reaction–diffusion systems in RN. We first show that there is a new entire solution for bistable reaction–diffusion systems which behaves as three moving planar fronts as time goes to -∞ and as a V-shaped traveling front as time goes to ∞. Then we address the speed of the interfaces corresponding to the entire solution by appealing to the super-sub solutions technique. Finally, we apply our results to two important models in biology.

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Entire solutions of monotone bistable reaction–diffusion systems in R^N

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