Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II
Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II
复制标题
具有自由边界的扩散逻辑模型中的扩散-消失二分法，II
DOI：
10.1016/j.jde.2011.02.011
复制
发表时间：
2011-06-15
影响因子：
2.4
通讯作者：
Guo, Zongming
中科院分区：
文献类型：
--
作者：
Du, Yihong;Guo, Zongming
研究了高维非均匀环境中具有自由边界的扩散Logistic方程。这样的模型可以用来描述新物种或入侵物种的扩散，自由边界代表扩展的前沿。为简单起见，我们假设环境和解是径向对称的。在一维空间和均匀环境的特殊情况下，Du和Lin(2010)[10]研究了这个自由边界问题。我们证明了Du和Lin(2010)[10]中建立的扩散-消失二分法在这里考虑的更一般和生态现实的背景下仍然成立。此外，当扩展发生时，我们得到了扩展锋面扩展速度的最佳可能的上下界。当环境在无穷远处渐近均匀时，这两个界限重合。我们的结果表明，该模型确定的渐近传播速度不依赖于空间维度。(C)2011 Elsevier Inc.保留所有权利。
We study the diffusive logistic equation with a free boundary in higher space dimensions and heterogeneous environment. Such a model may be used to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. For simplicity, we assume that the environment and the solution are radially symmetric. In the special case of one space dimension and homogeneous environment, this free boundary problem was investigated in Du and Lin (2010) [10]. We prove that the spreading-vanishing dichotomy established in Du and Lin (2010) [10] still holds in the more general and ecologically realistic setting considered here. Moreover, when spreading occurs, we obtain best possible upper and lower bounds for the spreading speed of the expanding front. When the environment is asymptotically homogeneous at infinity, these two bounds coincide. Our results indicate that the asymptotic spreading speed determined by this model does not depend on the spatial dimension. (C) 2011 Elsevier Inc. All rights reserved.