Reaction and Diffusion in the Presence of Fluid Flow

流体存在时的反应和扩散建议研究的摘要安德烈·兹拉托斯这个项目是研究对同时涉及反应和流体流动的系统进行建模的方程的数学分析。这将有助于我们理解内燃机燃烧、恒星核反应、森林火灾和大气中臭氧产生等问题。具体地说，我们将研究耦合到Navier-Stokes方程的反应扩散方程组。一个特殊的问题是分析由于流体平流的存在而导致的反应猝灭。另一个是对反应型Boussinesq系统的旅行前线的研究。这项工作将涉及到泛函分析，概率论和特殊技术的使用，包括谱理论和比较原理，对这些类型的非线性偏微分方程组。

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.