Mathematical Sciences: Research in Nonlinear Problems Arising in Mechanics

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9406295 Slemrod This proposal outlines proposed research in three areas: (i) kinetic modeling of gases exhibiting change of phase and metastable states, (ii) resolution of Riemann problems of hyperbolic systems of conservation laws via hydrodynamic and viscous limits, (iii) analysis of the structure of shock waves for spherically symmetric three dimensional fluid flow. The main goal is the understanding of the dynamics of these highly nonlinear phenomena and applying this insight to interpretation of the motivating physical problems. The technical approach to the above research will be to (i) examine cluster Boltzmann like dynamics and try to simulate van de Waals intermolecular attractions to develop discrete velocity phase transition models: (ii) apply self similar scaling methods to recover hydrodynamic and viscous limits for systems of conservation laws, (iii) impliment the viscous self similarity method to the analysis of spherically symmetric gas dynamics (conservation laws of mass, momentum, energy).