广义Fisher-Kolmogorov方程行波的新模式
New patterns of travelling waves in the generalized Fisher-Kolmogorov equation
摘要：
我们证明了一类退化（或奇异）拟线性抛物问题中行波族的存在性和唯一性，该问题可以看作是半线性Fisher-Kolmogorov-Petrovski-Piscounov方程在生物学中的推广.依赖于非线性扩散和非光滑反应函数之间的关系，我们精确地量化，我们调查行波的形状和渐近性质。我们的方法是基于半线性常微分方程的比较结果。
英文摘要：
We prove the existence and uniqueness of a family of travelling waves in a degenerate (or singular) quasilinear parabolic problem that may be regarded as a generalization of the semilinear Fisher-Kolmogorov-Petrovski-Piscounov equation for the advance of advantageous genes in biology. Depending on the relation between the nonlinear diffusion and the nonsmooth reaction function, which we quantify precisely, we investigate the shape and asymptotic properties of travelling waves. Our method is based on comparison results for semilinear ODEs.
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