Journal of Dynamics and Differential Equations ( IF 1.4 ) Pub Date : 2021-06-28 , DOI: 10.1007/s10884-021-10027-z Ningkui Sun , Chengxia Lei
This paper concerns the effect of the (separated/connected) protection zone for the evolution of an endangered species on the reaction–diffusion equation with the strong Allee effect and the free boundary. First, we describe the long-time dynamical behavior of the system of two types protection zones with the same length. Furthermore, the asymptotic profiles of solutions and the asymptotic spreading speed are estimated when spreading happens. Our results, together with those in previous papers Du et al. (J Differ Equ 266:7327–7356, 2019), Du and Lou (J Eur Math Soc 17:2673–2724, 2015) on two other closely related models, show that the protection zone and the free boundary play an important role in the evolution of the endangered species.
中文翻译:
具有强 Allee 效应和自由边界的反应扩散模型的长期行为:保护区的影响
本文关注(分离/连接)保护区对濒危物种进化的影响,具有强 Allee 效应和自由边界的反应扩散方程。首先,我们描述了两种长度相同的保护区系统的长期动态行为。此外,当传播发生时,估计解的渐近分布和渐近传播速度。我们的结果,连同之前 Du 等人的论文。(J Differ Equ 266:7327–7356, 2019)、Du 和 Lou (J Eur Math Soc 17:2673–2724, 2015) 在另外两个密切相关的模型中,表明保护区和自由边界在濒危物种的进化。