A diffusive logistic model with a free boundary in time-periodic environment

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• 作者：Yihong Du ; Zongming Guo ; Rui Peng
• 关键词：Diffusive logistic equation ; Free boundary ; Spreading&ndash ; vanishing dichotomy ; Periodic environment ; Spreading speed
• 刊名：Journal of Functional Analysis
• 出版年：2013
• 出版时间：1 November, 2013
• 年：2013
• 卷：265
• 期：9
• 页码：2089-2142
• 全文大小：474 K

文摘

We study the diffusive logistic equation with a free boundary in time-periodic 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 time independent environment, in the cases of one space dimension, and higher space dimensions with radial symmetry, this free boundary problem has been studied in Du and Lin (2010) , Du and Guo (2011) . In both cases, a spreading-vanishing dichotomy was established, and when spreading occurs, the asymptotic spreading speed was determined. In this paper, we show that the spreading-vanishing dichotomy is retained in time-periodic environment, and we also determine the spreading speed. The former is achieved by further developing the earlier techniques, and the latter is proved by introducing new ideas and methods.