Continuum Physics & Systems of Conservation Laws

DMS-9500574 Dafermos在双曲型守恒律系统的一般领域提出了一些项目。其中包括对一维空间中可容许弱解的几何结构的研究，以及在一维空间中由衰减记忆或摩擦引起的耗散情况下的大时间行为的研究，以及在多维空间中具有可交换雅可比的两个守恒律的双曲组理论的发展。拟议的研究是跨学科的，位于连续介质物理学和偏微分方程组理论之间的界面上。人们希望这项分析能为物理学提供一些启示，而作为回报，潜在的物理结构将指导和推动这项分析。连续介质物理学是经典物理学的一个分支，它将固体或流体材料建模为受守恒定律和本构假设支配的连续介质。所涉及的偏微分方程组是由弹性响应材料的守恒定律和本构假设产生的一阶拟线性双曲组。

DMS-9500574 Dafermos A number of projects are proposed, in the general area of hyperbolic systems of conservation laws. They include the study of the geometric structure of the admissible weak solutions and the investigation of the large time behavior in the presence of dissipation induced by fading memory or friction, in one space dimension; also the development of the theory of hyperbolic systems of two conservation laws with commuting Jacobians, in several space dimensions. The proposed research is interdisciplinary, lying on the interface between continuum physics and the theory of partial differential equations. The hope is that the analysis will shed some light on the physics and, in return, the underlying physical structure will direct and drive the analysis. Continuum physics is the branch of classical physics which models materials, solid or fluid, as continuous media governed by conservation laws and constitutive assumptions. The partial differential equations involved are first order quasilinear hyperbolic systems resulting from the conservation laws and constitutive assumptions of materials with elastic response.