Pulsating waves and entire solutions for a spatially periodic nonlocal dispersal system with a quiescent stage

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（12）
• 页码范围: 2505-2526
• 页数: 22页
• 语种: 英文

摘要

This paper deals with the pulsating waves and entire solutions for a spatially periodic nonlocal dispersal model with a quiescent stage.By the method of super-and subsolutions together with the comparison principle,we establish the existence of pulsating waves with any speed larger than the spreading speed.The construction of the super-and subsolutions depends on the principal eigenvalue theory for a periodic eigenvalue problem with partially degenerate nonlocal dispersal.The joint results of this paper and our recent work (Wang J B,Li W T,Sun J W.Global dynamics and spreading speeds for a partially degenerate system with non-local dispersal in periodic habitats.Proc Roy Soc Edinburgh Sect A,2018,148:849-880) show that the spreading speed coincides with the minimal wave speed of pulsating waves for the considered system.Moreover,combining the rightward and leftward pulsating waves with different speeds and a spatially periodic solution,we prove the existence and qualitative properties of entire solutions other than pulsating waves,which provide some new spreading ways in a heterogeneous habitat.