Continuum Physics & Systems of Conservation Laws

DMS-9500574 Dafermos在守恒律的双曲系统的一般领域提出了一些项目。他们包括研究的几何结构的容许弱解决方案和调查的大时间行为中存在的耗散引起的衰落记忆或摩擦，在一个空间维度;也发展理论的双曲系统的两个守恒律与交换雅可比矩阵，在几个空间维度。 拟议的研究是跨学科的，躺在连续介质物理和偏微分方程理论之间的接口。我们希望，分析将揭示一些物理学，作为回报，底层的物理结构将指导和驱动分析。连续介质物理学是经典物理学的分支，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是一阶拟线性双曲型方程组，它是由守恒定律和弹性材料的本构假设导出的。

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.