论文标题
定量陡度，半FKPP反应和Pushmi-Pullyu前线
Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts
论文作者
论文摘要
我们发现了大量反应扩散方程的看似以前未被注意到的代数结构，并尤其使用它来研究溶液的长时间行为及其在拉动和推动的方案中以及在Pushmi-Pullyu边界上的融合到行进波。本文中引入的一个新对象是形状缺陷函数，该函数间接地测量了溶液和行动波的轮廓之间的差异。尽管可以根据形状缺陷函数的阳性重新阐述“陡度”的经典概念，但令人惊讶的是，它的阳性可以以多种定量方式使用。特别是，阳性用于新的加权Hopf-Cole-Cole转换，以及在稳定参数中起关键作用的相对熵方法中使用的。形状缺陷函数还提供了在拉式推移过渡时反应扩散方程与反应保护定律之间的新联系。本文中的其他简单但看似新的代数结构散布在整个论文中。值得注意的是一种新的变分配方，它同样适用于拉动和推动的正面，在拉动情况下打开了对尚未难以捉摸的分析的门。
We uncover a seemingly previously unnoticed algebraic structure of a large class of reaction-diffusion equations and use it, in particular, to study the long time behavior of the solutions and their convergence to traveling waves in the pulled and pushed regimes, as well as at the pushmi-pullyu boundary. One such new object introduced in this paper is the shape defect function, which, indirectly, measures the difference between the profiles of the solution and the traveling wave. While one can recast the classical notion of `steepness' in terms of the positivity of the shape defect function, its positivity can, surprisingly, be used in numerous quantitative ways. In particular, the positivity is used in a new weighted Hopf-Cole transform and in a relative entropy approach that play a key role in the stability arguments. The shape defect function also gives a new connection between reaction-diffusion equations and reaction conservation laws at the pulled-pushed transition. Other simple but seemingly new algebraic constructions in the present paper supply various unexpected inequalities sprinkled throughout the paper. Of note is a new variational formulation that applies equally to pulled and pushed fronts, opening the door to an as-yet-elusive variational analysis in the pulled case.
