Transition fronts of time periodic bistable reaction-diffusion equations in R-N

Wei-Jie Sheng (1) , Hong-Jun Guo (2)

1 HIT Harbin Institute of Technology - Department of Mathematics
2 I2M - Institut de Mathématiques de Marseille

This paper is concerned with the existence and qualitative properties of transition fronts for time periodic bistable reaction-diffusion equations in R-N. We first show that any almost-planar transition front is actually planar, regardless of the number of transition layers. Then we prove that all transition fronts admit a global mean speed gamma and it holds gamma = vertical bar c vertical bar, where c is the speed of the planar traveling front. Finally we establish the existence of a transition front in R-N that is not a standard traveling front. Such a front behaves like three moving time periodic planar fronts as time goes to -infinity and like a time periodic V-shaped traveling front as time goes to infinity.

Mots clés: Bistable; Transition fronts; Time periodic; Reaction-diffusion equations

Domaines: Equations aux dérivées partielles [math.AP]

Wei-Jie Sheng, Hong-Jun Guo. Transition fronts of time periodic bistable reaction-diffusion equations in R-N. Journal of Differential Equations, 2018, 265 (5), pp.2191-2242. ⟨10.1016/j.jde.2018.04.032⟩. ⟨hal-02075267⟩