Mathematical Sciences: Nonlinear Reaction-Diffusion

研究了两个反应扩散问题 一个来自化学工程，一个来自气候学， 表现出自由的或移动的边界。 第一个问题是 反应器中的分数阶放热反应，或 催化剂颗粒 可能存在一个死核心（一个区域 其中反应物浓度为零），其边界演变 及时 特别注意一种高浓度的化学物质 扩散率近似称为阴影系统。 第二 问题处理流体和固体相之间的相互作用， 化学和材料中常见的现象 工程.多孔介质燃烧的各种特性 固体进行了研究，如转化时间，转化率 前面，和渗透前面。 所谓的有效性 伪稳态近似检查在一个更一般的 比以前考虑的要好。 气候学问题 关注冰层覆盖区域对参数的依赖性， 太阳常数和红外辐射常数 出现在能量平衡方程中。 本研究涉及反应扩散系统的一些方面。 这个名字起源于一些问题，如燃烧。 当氧气通过热煤扩散并与煤反应时， 将其转化为产品。 了相应的数学 模型也会在其他设置中显示，但会进行一些修改： 比如说催化转化器，生态竞争， 在污染物的扩散和清除中， 脉冲沿着神经的传播，以及气候建模。 研究者的兴趣在于数学 框架和具体应用。 使用技术 最近开发的，他将努力获得估计 对于物理感兴趣的量，例如 在气-固反应中固体的转化， 地球上的冰盖的影响， 大气中的温室气体。

The investigator studies two reaction-diffusion problems arising in chemical engineering and one from climatology, each exhibiting a free or moving boundary. The first problem concerns an exothermic reaction of fractional order in a reactor or catalyst particle. There may then exist a dead core (a region where the reactant concentration vanishes) whose boundary evolves in time. Particular attention is paid to a high chemical diffusivity approximation known as the shadow system. The second problem treats the interaction between fluid and solid phases, a frequent phenomenon in chemical and materials engineering. Various properties of the combustion of a porous solid are studied, such as the conversion time, the conversion front, and the penetration front. The validity of the so-called pseudo-steady-state approximation is examined in a more general setting than previously considered. The climatology problem concerns the dependence of ice-covered regions on parameters such as the solar constant and the infrared radiation constants that appear in the energy balance equation. This study deals with aspects of reaction-diffusion systems. The name originated with problems such as the combustion of coal as oxygen diffuses through the hot coal and reacts with it, converting it to products. The corresponding mathematical model also appears, with some modifications, in other settings: for instance, in catalytic converters, in ecological competition, in the spreading of contaminants and in their removal, in propagation of impluses along nerves, and in climate modeling. The investigator's interest lies both in the mathematical framework and in specific applications. Using techniques developed recently, he directs his efforts to obtaining estimates for quantities of physical interest such as the time required for conversion of the solid in a gas-solid reaction and to finding the effect on the earth's icecaps of a change in the amount of greenhouse gases in the atmosphere.