Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations
Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations
复制标题
一维反应扩散方程中传播平台的存在性和收敛性
DOI：
10.1090/s0002-9947-2014-06105-9
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
H. Matano
中科院分区：
文献类型：
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作者：
A. Ducrot;T. Giletti;H. Matano
考虑一类具有空间周期非线性项（包括多稳定项）的一维反应扩散方程，研究了Heaviside型初值下解的渐近性态.我们的分析揭示了一些新的动力学，其中传播的轮廓不是由单个正面表征的，而是由我们称之为阶地的多个正面的层表征的。存在性和收敛到这样的平台证明了使用交叉数参数，而不太依赖于标准的线性分析。因此，在我们的工作突出的特殊现象的传播，几个推论将遵循的存在和收敛到脉动的旅行前，即使是高度退化的非线性，以前没有处理。引用
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities–including multi-stable ones–and study the asymptotic behavior of solutions with Heaviside type initial data. Our analysis reveals some new dynamics where the profile of the propagation is not characterized by a single front, but by a layer of several fronts which we call a terrace. Existence and convergence to such a terrace is proven by using an intersection number argument, without much relying on standard linear analysis. Hence, on top of the peculiar phenomenon of propagation that our work highlights, several corollaries will follow on the existence and convergence to pulsating traveling fronts even for highly degenerate nonlinearities that have not been treated before. References