Continuum Physics & Systems of Conservation Laws

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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.