Analysis and computation of nonlinear hyperbolic problems

守恒定律是许多应用的连续模型，例如非线性弹性，广义相对论中的冲击波和工厂中的工作流程，但历史上它们主要作为可压缩流体流动的模型进行研究。作为连续介质模型，非线性双曲守恒律作为分子、动力学（统计）和高阶模型的标度极限出现。然而，由此产生的模型是不稳定的，在缩放中丢失的一些物理需要重新引入，通常是熵条件，动力学关系和可能的额外封闭。

Conservation laws are continuum models for many applications such as nonlinear elasticity, shock waves in general relativity and workflow in factories, but, historically they were primarily studied as models of compressible fluid flow. As continuum models, nonlinear hyperbolic conservation laws occur as scaling limits of molecular, kinetic (statistical) and higher-order models. Invariably, the resulting models are unstable and some of the physics lost in the scaling needs to be re-introduced, typically with an entropy condition, a kinetic relation and possibly additional closures.