On the Homogenization of some Free Boundary Problems

关于某些自由边界问题的均匀化问题研究摘要antoine mellet主要研究人员提出分析某些自由边界问题的一些性质。本文的目的是研究这些问题的均质性。均质化的目的是描述介质局部性质的微小变化对解的整体行为的影响。在过去的三十年里，均质理论得到了广泛的发展，但很少有工作涉及自由边界问题。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。该提议的一部分处理了一滴液体在斜面上的运动问题——比如水在窗户上的运动。众所周知，这是一个困难的数学问题，在许多领域都有应用，包括油漆的涂抹和农药喷洒在植物叶子上的保留。PI在火焰传播分析中研究了这类问题，他的工作导致了对观察到的各种问题的理解，包括火焰锋面的传播。

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.