Long time behavior for solutions of the diffusive logistic equation with advection and free boundary

作者：Wei, Lei; Zhang, Guanghui^*; Zhou, Maolin

来源：Calculus of Variations and Partial Differential Equations, 2016, 55(4): 95.

DOI：10.1007/s00526-016-1039-y

• SPEED
• MODEL
• HABITAT
• FRONT

We consider the influence of a shifting environment and an advection on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When the environment is shifting and without advection (beta = 0), Du et al. (Spreading in a shifting environment modeled by the diffusive logistic equation with a free boundary. arXiv:1508.06246, 2015) showed that the species always dies out when the shifting speed c(*) >= C, and the long-time behavior of the species is determined by trichotomy when the shifting speed c(*) is an element of (0, C). Here we mainly consider the problems with advection and shifting speed c(*) is an element of (0, C) (the case c(*) >= C can be studied by similar methods in this paper). We prove that there exist beta* < 0 and beta(*) > 0 such that the species always dies out in the long-run when beta <= beta*, while for beta is an element of (beta*, beta(*)) or beta = beta(*), the long-time behavior of the species is determined by the corresponding trichotomies respectively.

• 出版日期2016-8
• 单位华中科技大学; 江苏师范大学