Reaction and Diffusion in the Presence of Fluid Flow

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Reaction and Diffusion in the Presence of Fluid FlowAbstract of Proposed ResearchAndrej Zlatos This project is to investigate the mathematical analysis of equations that model systems that involve both reactions and fluid flow. This will help our understanding of issues such as burning in internal combustion engines, nuclear reactions in stars, forest fires and the production of ozone in the atmosphere. Specifically we shall study systems of reaction diffusion equations coupled to the Navier-Stokes equation. A particular problem is to analyze the quenching of reaction due to the presence of fluid advection. Another is the study of traveling fronts for the reactive Boussinesq system. This work will involves the use of functional analysis, probability theory and special techniques, including spectral theory and comparison principles, for these classes of nonlinear partial differential equations.