Mathematical Sciences: Convergence of Approximate Solutions to Conservation Laws

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The mathematical theory of discontinuous solutions to hyperbolic systems is developing intensively motivated by problems from continuum physics which model reactive flows, multiphase flows, and elastoplastic flows, for example. The principal investigator will focus on methods of approximation for these problems and their convergence to physical discontinuous solutions. A better understanding of the methods of numerical approximation for some fundamental hyperbolic problems arising in continuum physics has profound real world implications. These ideas carry over to such initiatives as materials processing.