Asymptotic behavior of solutions of a free boundary model with seasonal succession and impulsive harvesting

Abstract

In this article, we consider the influence of seasonal succession and impulsive harvesting on the dynamical behavior of solutions to a free boundary model. First, the generalized principal eigenvalue is defined and its properties are studied. Next, some sufficient conditions for spreading and for vanishing are given. Then, by introducing a one-parameter family of initial data σϕ\sigma \phi with σ≥0\sigma \ge 0 and ϕ\phi being a compactly supported function, we obtain a threshold value σ*{\sigma }^{* } such that spreading happens when σ>σ*\sigma \gt {\sigma }^{* }, vanishing happens when σ≤σ*\sigma \le {\sigma }^{* }. Finally, we prove the existence and uniqueness of TT-periodic traveling semi-wave. Moreover, when spreading persists, we use the proved TT-periodic traveling semi-wave to estimate the asymptotic speed of the free boundaries.

Keywords

• reaction-diffusion equation
• asymptotic behavior of solutions
• free boundary problem
• impulsive harvesting
• seasonal succession
• 35k20
• 35k57
• 35r35
• 35b40