On the Homogenization of some Free Boundary Problems

关于一些自由边界问题的均匀化建议研究摘要Antoine Mellet主要研究者建议分析某些自由边界问题的一些性质。本建议就是要研究这些问题的同质化。均匀化的目的是描述介质局部性质的微小变化对解的全局行为的影响。在过去的三十年里，均匀化理论得到了广泛的发展，但很少有研究自由边界问题，自由边界问题在涉及界面的生物和物理现象的建模中自然出现。这里提出的工作将使用均匀化来研究界面的形状。该提案的一部分涉及一滴液体在倾斜平面上的运动问题-例如水在窗户上。众所周知，这是一个很难的数学问题，在许多领域都有应用，包括油漆的传播和农药喷雾在植物叶子上的保留。PI在火焰传播分析中研究了这种类型的问题，他的工作使人们了解了观察到的各种问题，包括火焰前沿的传播。

On the Homogenization of some Free Boundary ProblemsAbstract of proposed researchAntoine MelletThe principal investigator proposes to analyze some properties of certain free boundary problems. This proposal is to study the homogenization of these problems. The aim of homogenization is to describe the influence of small variations in the local properties of the medium on the global behavior of the solutions. There has been extensive development in the theory of homogenization over the last thirty years but very little of the work has treated free boundary problems.Free boundary problems arise naturally in the modeling of biological and physical phenomena involving an interface. The work proposed here will use homogenization to study the shapes of interfaces. Part of the proposal treats the problem of the motion of a drop of liquid on an inclined plane - such as water on a window. This is known to be a difficult mathematical problem and has applications in many areas including the spreading of paint and the retention of pesticide sprays on plant leaves. The PI has studied problems of this type in the analysis of flame propagation and his work has led to an understanding of various issues observed there including the propagation of flame fronts.