论文标题
非lipschitz多稳态非线性的露台解决方案
Terrace solutions for non-Lipschitz multistable nonlinearities
论文作者
论文摘要
对于Lipschitz的连续单位和可动反应函数，对反应扩散方程的行进波解非常研究。这些特殊解决方案在数学生物学，尤其是生态入侵研究中起着关键作用。但是，如果有两个以上稳定的稳态，那么入侵现象可能会变得更加复杂并涉及中间步骤，这会导致一个人认为不是一个单一的，而是以有序速度的一系列行进波。在本文中，我们表明，如果反应函数在稳定的稳态处是不连续的，那么存在这样的行进波，甚至提供了一种特殊的解决方案，我们称之为露台解决方案。更确切地说，我们将解决露台解决方案的存在和独特性。
Traveling wave solutions of reaction-diffusion equations are well-studied for Lipschitz continuous monostable and bistable reaction functions. These special solutions play a key role in mathematical biology and in particular in the study of ecological invasions. However, if there are more than two stable steady states, the invasion phenomenon may become more intricate and involve intermediate steps, which leads one to consider not a single but a collection of traveling waves with ordered speeds. In this paper we show that, if the reaction function is discontinuous at the stable steady states, then such a collection of traveling waves exists and even provides a special solution which we call a terrace solution. More precisely, we will address both the existence and uniqueness of the terrace solution.
