Mathematical Sciences: Shock Waves and Conservation Laws

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The principal investigator will conduct research in the area of nonlinear conservation laws and shock waves, continuing the study of elementary waves and the Riemann problem in resonant nonlinear systems as well as the convergence properties of numerical methods utilizing this construction. Shock waves are the observed in many "flow" situations. The presence of steep gradients leads to serious difficulties in both theoretical and numerical methods for obtaining solutions. The qualitative and quatitative analysis of nonlinear waves is of significant scientific interest in view of the wide spread occurrence of such phenomena in real world situations.