scholarly journals Diffusive KPP equations with free boundaries in time almost periodic environments: II. Spreading speeds and semi-wave solutions

2016 ◽  
Vol 261 (4) ◽  
pp. 2403-2445 ◽  
Author(s):  
Fang Li ◽  
Xing Liang ◽  
Wenxian Shen
Keyword(s):  
Almost Periodic ◽  
Free Boundaries ◽  
Spreading Speeds ◽  
Wave Solutions ◽  
Kpp Equations ◽  
Periodic Environments

scholarly journals Spreading speeds and traveling wave solutions in cooperative integral-differential systems

2015 ◽  
Vol 20 (6) ◽  
pp. 1663-1684 ◽  
Author(s):  
Changbing Hu ◽  
◽  
Yang Kuang ◽  
Bingtuan Li ◽  
Hao Liu ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Spreading Speeds ◽  
Differential Systems ◽  
Wave Solutions

scholarly journals Long-time behavior of random and nonautonomous Fisher-KPP equations. Part II. Transition fronts

2019 ◽  
Vol 19 (06) ◽  
pp. 1950046 ◽  
Author(s):  
Rachidi B. Salako ◽  
Wenxian Shen
Keyword(s):  
Time Behavior ◽  
Long Time Behavior ◽  
Spreading Speeds ◽  
Kpp Equation ◽  
Random Transition ◽  
Existence And Stability ◽  
Long Time ◽  
Kpp Equations ◽  
The Stability ◽  
Transition Fronts

In the current series of two papers, we study the long-time behavior of the following random Fisher-KPP equation: [Formula: see text] where [Formula: see text], [Formula: see text] is a given probability space, [Formula: see text] is an ergodic metric dynamical system on [Formula: see text], and [Formula: see text] for every [Formula: see text]. We also study the long-time behavior of the following nonautonomous Fisher-KPP equation: [Formula: see text] where [Formula: see text] is a positive locally Hölder continuous function. In the first part of the series, we studied the stability of positive equilibria and the spreading speeds of (1.1) and (1.2). In this second part of the series, we investigate the existence and stability of transition fronts of (1.1) and (1.2). We first study the transition fronts of (1.1). Under some proper assumption on [Formula: see text], we show the existence of random transition fronts of (1.1) with least mean speed greater than or equal to some constant [Formula: see text] and the nonexistence of random transition fronts of (1.1) with least mean speed less than [Formula: see text]. We prove the stability of random transition fronts of (1.1) with least mean speed greater than [Formula: see text]. Note that it is proved in the first part that [Formula: see text] is the infimum of the spreading speeds of (1.1). We next study the existence and stability of transition fronts of (1.2). It is not assumed that [Formula: see text] and [Formula: see text] are bounded above and below by some positive constants. Many existing results in literature on transition fronts of Fisher-KPP equations have been extended to the general cases considered in the current paper. The current paper also obtains several new results.

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