Mathematical Sciences: Hyperbolic Analysis: Wave Interactionand Chaos

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This proposal is concerned with research in theoretical and computational nonlinear wave interaction problems and the chaotic mixing associated with unstable interface-wave interactions. Mathematical theory of hyperbolic equations will be developed and will be used to the maximum extent possible within the computational procedure. Reversing this process, computation will be used as a support to the development of mathematical theory. Such theoretical developments are basic inputs to front tracking computations, which allow high resolution study multidimensional wave interactions. Chaotic flow regimes require stochastic models, which are tested using high resolution front tracking techniques.