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演化型偏微分方程相关的数学问题，包括一些作为相变模型的自由边界问题，以及Landau-Stuart方程缺陷解的动力学。将研究Cahn-Hilliard方程的推广和相关的自由边值问题，以帮助理解成核、生长和粗化现象。这种自由边值问题的定性分析将解释在某些空间均质二元合金中发生的相分离现象。鉴于这种现象在现实世界中广泛存在，这类研究具有重要的科学意义。

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.