Wave Solutions to Reaction-Diffusion Systems in Perforated Domains
Wave Solutions to Reaction-Diffusion Systems in Perforated Domains
复制标题
穿孔域中反应扩散系统的波解
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
S. Heinze
中科院分区：
文献类型：
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作者：
S. Heinze
证明了当齐次化方程允许非简并的行波时，周期穿孔域中的行波对于大类反应扩散系统是存在的。这可以应用于例如具有双稳非线性的单方程和双稳单调系统。该证明利用了H空间中一个适当变换问题的隐函数定理，并给出了波型和波速的校正型估计。
Traveling waves in periodically perforated domains are shown to exist for large classes of reaction-diffusion systems, provided the homogenized equation admits a non-degenerate traveling wave. This can be applied e.g. to a single equation with bistable non-linearity and to bistable monotone systems. The proof uses the implicit function theorem of a suitably transformed problem in the space H. Furthermore, corrector-type estimates are given for the wave profile and the wave velocity.