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

本研究涉及与相变，特别是相分离模型有关的数学问题。现有的相分离模型是Cahn-Hilliard方程（用于二元合金）和相场方程（用于具有潜热的纯材料）。数学问题与初始相分离事件和随后的材料粗化有关。此外，研究将包括研究不同静止状态之间的联系，在一个案例中，研究内层的运动，这是粗化后期的特征。研究方向是应用数学的一般领域和相变动力学的特定领域的数学模型。该项目由四名研究人员组成。

This research concerns mathematical questions relating to models for phase change, especially phase separation. The existing models for phase separation are the Cahn-Hilliard equation (for a binary alloy) and the phase field equations (for a pure material with latent heat). The mathematical issues relate to the initial phase separation events and the subsequent coarsening of the material. Also, the research will include a study of the connections between different stationary states and, in one case, the motion of internal layers, characteristic of the later stages of coarsening. The research is in the general area of applied mathematics and in the specific area mathematical models for the dynamics of phase changes. The project supports a group effort of four researchers.