Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed
Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed
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由具有自由边界的单稳态方程控制的时空周期性介质中的传播，第 2 部分：传播速度
DOI：
10.1016/j.anihpc.2019.01.005
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发表时间：
2019
影响因子：
1.9
通讯作者：
Liang Xing
中科院分区：
文献类型：
--
作者：
Ding Weiwei;Du Yihong;Liang Xing
这是我们工作的第二部分，旨在对时空周期介质中具有单稳态反应项的自由边界问题的解的长时间行为进行分类。在第一部分（见[2]）中，我们建立了一个关于这类具有连续初始函数的自由边值问题解的存在唯一性的理论，以及一个扩张-消失二分法。我们现在能够发展Weinberger [15]，[16]和其他人[6]，[7]，[8]，[9]，[10]的方法来证明当扩展发生时渐近扩展速度的存在性，而无需先验地知道自由边界问题相应的半波解的存在性。这是一个完全不同的方法，从早期的作品中的自由边界模型，其中的传播速度是通过首先显示存在一个相应的半波。这样的半波似乎很难获得的情况下，在我们的工作考虑在这里的时空周期介质的早期方法。
This is Part 2 of our work aimed at classifying the long-time behavior of the solution to a free boundary problem with monostable reaction term in space–time periodic media. In Part 1 (see [2]) we have established a theory on the existence and uniqueness of solutions to this free boundary problem with continuous initial functions, as well as a spreading-vanishing dichotomy. We are now able to develop the methods of Weinberger [15], [16] and others [6], [7], [8], [9], [10] to prove the existence of asymptotic spreading speed when spreading happens, without knowing a priori the existence of the corresponding semi-wave solutions of the free boundary problem. This is a completely different approach from earlier works on the free boundary model, where the spreading speed is determined by firstly showing the existence of a corresponding semi-wave. Such a semi-wave appears difficult to obtain by the earlier approaches in the case of space–time periodic media considered in our work here.