论文标题
变异原理的等效性，以确定标量反应扩散前线的速度
Equivalence of variational principles to determine the speed of scalar reaction diffusion fronts
论文作者
论文摘要
标量反应扩散方程的行进前线速度的确定已成为大量研究的主题。使用了看似断开变化原理的不同方法。这项工作的目的是显示它们之间的联系。对于单一的反应术语，我们证明了Hadeler和Rothe于1975年建立的原则，以及1996年Benguria和Depassier的第二个原则在逻辑上是等效的，也就是说，可以从另一个中得出。证明了针对任意反应项制定的两个变异原理通过适当的变量更改而言。最后，一个可单稳性反应项证明的变异原理被证明是在另一个独立变量中的两个之前的公式。
The determination of the speed of travelling fronts of the scalar reaction diffusion equation has been the subject of much study. Using different approaches seemingly disconnected variational principles have been established. The purpose of this work is to show the connection between them. For monostable reaction terms, we prove that a principle established by Hadeler and Rothe in 1975 and a second one by Benguria and Depassier in 1996 are logically equivalent, that is, either can be derived from the other. Two variational principles, formulated for arbitrary reaction terms, are shown to be related by a suitable change of variables. Finally a variational principle proven for monostable reaction terms is shown to be a formulation of the two previous ones in yet another independent variable.
