论文标题
将Lagrangian转换扩展到非凸标量保护法
Extending Lagrangian transformations to nonconvex scalar conservation laws
论文作者
论文摘要
本文研究了一种以粒子路径的形式找到拉格朗日转换的方法，以使所有具有光滑通量的标量保护定律。使用弱差异性的概念发现了这些。更确切地说，根据任何给定的标量保护法，我们得出了一个线性退化和一个真正非线性家庭的寺庙系统。我们修改系统以使其严格夸张，并证明其存在结果。最后，我们确定该系统的熵弱解决方案等效于标量方程的解决方案。该方法还决定了相关的弱差异性。
The present paper studies a method of finding Lagrangian transformations, in the form of particle paths, for all scalar conservation laws having a smooth flux. These are found using the notion of weak diffeomorphisms. More precisely, from any given scalar conservation law, we derive a Temple system having one linearly degenerate and one genuinely nonlinear family. We modify the system to make it strictly hyperbolic and prove an existence result for it. Finally we establish that entropy admissible weak solutions to this system are equivalent to those of the scalar equation. This method also determines the associated weak diffeomorphism.
