Reaction and Diffusion in the Presence of Fluid Flow

拟建研究摘要andrej Zlatos本项目旨在研究同时涉及反应和流体流动的系统模型的数学分析。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的产生等问题。具体来说，我们将研究与Navier-Stokes方程耦合的反应扩散方程系统。一个特殊的问题是分析由于流体平流的存在而引起的反应的猝灭。另一项研究是对反应式Boussinesq系统行进锋面的研究。这项工作将涉及使用泛函分析，概率论和特殊技术，包括谱理论和比较原理，这类非线性偏微分方程。

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.