Mathematical Sciences: Stability for Reaction-diffusion Equations

该项目将遵循两条调查路线， 应用数学问题。 第一个是 了解相变的数学模型 现象。 这些问题具有变分结构， 研究椭圆或抛物方程的区别解 具有小扩散系数的方程。 第二类 的工作将集中在进化系统， 必须是变分类型的，并且保持顺序。 一 主要目的是确定所有的渐近性质 解决方案 将研究联系在一起的一个共同主题是 问题涉及反应扩散机制， 分析采用稳定性考虑。 从应用 第一个项目试图建立某些模型， 可观察到的模式，无论是稳定的平衡或不稳定的 流形的平衡;第二个试图排除 一类受迫系统稳定混沌的可能性， 建立非常规范的行为准则。

This project will follow two lines of investigation into problems of applied mathematics. The first is that of understanding certain mathematical models for phase transition phenomena. The problems have a variational structure and involve the study of distinguished solutions for elliptic or parabolic equations with small diffusion coefficients. The second category of work will concentrate on evolution systems that are not necessarily of variational type and which preserve order. One main objective is to determine asymptotic properties of all solutions. A common theme which ties the research together is that the problems deal with reaction-diffusion mechanisms and that the analysis employs stability considerations. From the applications point of view, the first project seeks to model certain observable patterns either as stable equilibria or as unstable manifolds of equilibria; the second seeks to exclude the possibility of stable chaos for classes of forced systems and to establish very regular behavior criteria.