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

主要研究人员将研究一些与发展型非线性偏微分方程有关的数学问题，包括一些作为相变模型而产生的自由边界问题，以及Landau-Stuart方程的亏损解的动力学。我们将研究Cahn-Hilliard方程和相关的自由边值问题的推广，以帮助理解成核、生长和粗化现象。对这类自由边值问题的定性分析将解释某些空间均匀二元合金中出现的相分离现象。鉴于在现实世界中广泛发生的情况，这种研究具有重大的科学意义。

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.