Mathematical Sciences Research Institute

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Seminar

Selection and existence of solutions for several free boundary problems May 17, 2011 (10:00 AM PDT - 12:00 PM PDT)
Parent Program: -- MSRI: Baker Board Room
Speaker(s) Xuming Xie
Description No Description
Video
There are a class of physical problems that involve selection. In this class of problems, when some parameter $\epsilon$ (such as surface tension ) is zero, there are a continuum set of solutions. However, as $\epsilon$ is NOT zero , only a discrete set of solutions exist. In this talk, we are going to survey some rigorous results in selection and existence for several free boundary problems such as viscous fingering and dendritic crystal growth. We will explain the selection mechanism for these physical problems and how it could be applied to the related linear stability problem. Some results are joint work with Saleh Tanveer.