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, ...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.展开更多
基金supported by the Scientific Research Start-up Fee for High-level Talents(Grant No.162301182740)National Natural Science Foundation of China(Grant Nos.11731005,11671180and 11901543)
文摘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.
