Structure of Entropy Solutions for Multi-Dimensional Scalar Conservation Laws
Structure of Entropy Solutions for Multi-Dimensional Scalar Conservation Laws
复制标题
多维标量守恒定律的熵解的结构
DOI：
--
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Michael Westdickenberg
中科院分区：
文献类型：
--
作者：
Camillo De Lellis;F. Otto;Michael Westdickenberg
摘要：多维标量守恒律的熵解u不一定在BV中，即使守恒律确实是非线性的。我们证明了u仍然具有BV函数的结构，在这个意义上激波位置是余维一可校正的。这一结果定性地突出了真非线性的正则化效应；它是基于局部有限的熵耗散速率的。证明依赖于动力学公式框架中爆破的几何分类。
Abstract.An entropy solution u of a multi-dimensional scalar conservation law is not necessarily in BV, even if the conservation law is genuinely nonlinear. We show that u nevertheless has the structure of a BV function in the sense that the shock location is codimension-one rectifiable. This result highlights the regularizing effect of genuine nonlinearity in a qualitative way; it is based on the locally finite rate of entropy dissipation. The proof relies on the geometric classification of blow-ups in the framework of the kinetic formulation.