Hyperbolic Conservation Laws in Continuum Physics

美国国家科学基金会奖摘要- DMS-0103730数学科学：连续介质物理中的双曲守恒律摘要0103730 Dafermos该研究计划基于连续介质物理学和双曲守恒律系统理论之间的界面。 它包括以下两个方面：（a）研究仅有界可测但变差不一定有界的双曲型守恒律弱解的几何结构;（B）研究非线性双曲性和由粘性或电磁效应引起的阻尼之间相互作用的学科。双曲守恒律是控制非线性系统的动力学行为的非线性偏微分方程组。具有非线性弹性响应的材料，如空气、橡胶等。非线性引起了作为冲击波传播的不连续性的发展。 该研究项目将调查在何种程度上可以通过粘性或电磁效应引起的阻尼机制来抑制冲击的不稳定作用。

NSF Award Abstract - DMS-0103730Mathematical Sciences: Hyperbolic Conservation Laws in Continuum PhysicsAbstract0103730 DafermosThe research program lies on the interface between continuum physics and the theory of hyperbolic systems of conservation laws. It involves the following two projects: (a) the study of the geometric structure of weak solutions to hyperbolic conservation laws that are merely bounded and measurable but not necessarily of bounded variation; (b) the study of the interaction between nonlinear hyperbolicity and damping induced by viscous or electromagnetic effects.Hyperbolic conservation laws are nonlinear systems of partial differential equations that govern the dynamic behavior of materials with nonlinear elastic response, such as air, rubber etc. Nonlinearity induces the development of discontinuities propagating as shock waves. The research project will investigate to what extent the destabilizing action of shocks may be checked by damping mechanisms induced by viscous or electromagnetic effects.