Mathematical Sciences: Systems of Nonlinear Conservation Laws

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This research program is concerned with the theoretical and numerical study of systems of nonlinear partial differntial equations which change type by losing strict hyperbolicity. Specific efforts include the adaptation and implementation of the emerging shock capturing numerical methods of high accuracy. This involves the approximate solution of generalized Riemann problems for which recent theoretical insights obtained by the PI will be used. Constitutive laws leading to equations of mixed type will also be investigated. Results from this research program will have applications in the areas of multiphase flows, elastic solids and magneto- hydrodynamics.