Hyperbolic Conservation Laws in Continuum Physics

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NSF Award Abstract - DMS-0103730Mathematical Sciences: Hyperbolic Conservation Laws in Continuum PhysicsAbstract0103730 DafermosThe 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.