Hyperbolic Conservation Laws in Continuum Physics

Brown University, Providence RI

Investigators

Abstract

NSF Award Abstract - DMS-0103730 Mathematical Sciences: Hyperbolic Conservation Laws in Continuum Physics Abstract 0103730 Dafermos The 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.