Irregular Behavior of Solutions for Fisher’s Equation
Irregular Behavior of Solutions for Fisher’s Equation
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DOI：
10.1007/s10884-007-9096-8
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发表时间：
2007-10
影响因子：
1.3
通讯作者：
E. Yanagida
中科院分区：
文献类型：
--
作者：
E. Yanagida
本文研究了当初始数据在空间无穷远处不以规则方式衰减时Fisher方程解的不规则性态。在一维的情况下，我们证明了一个解决方案的存在性，其轮廓和平均速度是不收敛的。在高维的情况下，我们证明了存在的扩展前与任意规定的配置文件。我们还表明，存在不规则的扩展锋，其轮廓随时间而变化。证明是基于两个不同的解决方案和比较技术的差异的一些估计。
This paper is concerned with the irregular behavior of solutions for Fisher’s equation when initial data do not decay in a regular way at the spatial infinity. In the one-dimensional case, we show the existence of a solution whose profile and average speed are not convergent. In the higher-dimensional case, we show the existence of expanding fronts with arbitrarily prescribed profiles. We also show the existence of irregularly expanding fronts whose profile varies in time. Proofs are based on some estimate of the difference of two distinct solutions and a comparison technique.