This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. In an abstract setting, we establish the existence of traveling waves for discrete and continuous-time monotone semiflows in homogeneous and periodic habitats. The results are then extended to monotone semiflows with weak compactness. We also apply the theory to four classes of evolution systems.
Cite this article
Jian Fang, Xiao-Qiang Zhao, Bistable traveling waves for monotone semiflows with applications. J. Eur. Math. Soc. 17 (2015), no. 9, pp. 2243–2288DOI 10.4171/JEMS/556