Continuum Physics & Systems of Conservation Laws

连续体物理

• 批准号: 9500574
• 负责人: Constantine Dafermos
• 金额: $ 13.5万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500574&HistoricalAwards=false
• 关键词: Continuum; Physics; & Systems; Conservation

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.

DMS-9500574 Dafermos在守恒定律的双曲系统的一般领域提出了许多项目。它们包括对可容许弱解的几何结构的研究，以及在一维空间中由记忆衰退或摩擦引起的耗散存在时的大时间行为的研究；以及在若干空间维度上具有交换雅可比矩阵的两个守恒律的双曲系统理论的发展。提出的研究是跨学科的，位于连续介质物理和偏微分方程理论之间的界面。我们的希望是，分析将揭示一些物理，作为回报，潜在的物理结构将指导和推动分析。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作为受守恒定律和本构假设支配的连续介质进行建模。所涉及的偏微分方程是由具有弹性响应的材料的守恒定律和本构假设所产生的一阶拟线性双曲方程组。