Mathematical Sciences: Conservation Laws that Change Type

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8903768 Keyfitz This project is concerned with the mathematical properties and applications of systems of conservation laws that are not of classical, strictly hyperbolic type. Models with these unusual features may be used to describe a variety of complex flows in continuum mechanics, including visco-elastic and visco-plastic fluids, flow in mixtures undergoing phase transitions in fluids and in solid elasticity, and porous-medium flows; similar equations appear in models for granular flows. In recent research, the principal investigator has identified some mathematical properties distinguishing different models; these include degree of separation of the wave speeds, behavior of the speeds where the type changes, and other qualitative properties of the wave curves. She plans to examine how these properties affect well-posedness, and to study stability of solutions under higher-order perturbations. Studies will also be made of models that appear in specific applications, and the conclusions, including algorithms for numerical computation, will be applied to multidimensional conservation laws.