Mathematical Sciences: Nonlinear Partial Differential Equations and Models for Phase Change

首席研究员将研究一些 与非线性偏微分有关的数学问题 包含自由边界的发展型方程 作为相变模型出现的问题，以及动力学 Landau-Stuart方程的缺陷解。 Cahn-Hilliard方程的推广及相关的 自由边界值问题将被研究，以帮助理解 形核、生长和粗化现象。 这种自由边值的定性分析 这些问题将解释在一些实施例中发生的相分离。 空间均匀二元合金 这些研究是 鉴于广泛的传播， 发生在真实的世界的情况。

The principal investigator will study a number of mathematical questions relating to nonlinear partial differential equations of evolution type, including some free boundary problems arising as models for phase transition, and the dynamics of defect solutions of the Landau-Stuart equation. Generalizations of the Cahn-Hilliard equation and associated free-boundary value problems will be studied to help understand the phenomena of nucleation, growth, and coarsening. The qualitative analysis of such free boundary value problems will explain the phase separation which occurs in some spatially homogeneous binary alloys. Such studies are of significant scientific interest in view of the wide spread occurrence in real world situations.