Spreading-vanishing dichotomy in a degenerate logistic model with general logistic nonlinear term

Boundary value problems

Xuesong Dong¹  Yanghui Li²  Kevin Sun²  Haiquan Qiao²  Lixin Ma²  Xian Jiang² 

[1] College of Automation, Harbin Engineering University, Harbin, P.R. China;The 1st Affiliated Hospital of Harbin Medical University, Harbin, P.R. China

关键词: logistic equation;    free boundary problem;    spreading-vanishing dichotomy;    invasion ecology;   

DOI  :  10.1186/s13661-014-0180-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the degenerate logistic equation with a free boundary and general logistic term in higher space dimensions and heterogeneous environment, which is used to describe the spreading of a new or invasive species. We first prove the existence and uniqueness of the local solution for the free boundary problem by the contraction mapping theorem, then we show that the solution can be expanded to all time using suitable estimates. Finally, we prove the spreading-vanishing dichotomy.

【 授权许可】

CC BY