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홈 > 학술정보 >학술행사 > 세미나
KAIST PDE 세미나

Title
Generation of interface for solutions of the mass-conserved Allen-Cahn equation
Speaker
Thanh Nam NGUYEN   (NIMS )
Date
2017-05-02 17:00:00
Host
KAIST
Place
자과동 Room 1409
Abstract
In this talk we discuss the generation of interface property for solutions of the nonlocal Allen-Cahn equation which was proposed by Rubinstein and Sternberg as a model for phase separation in a binary mixture. More precisely, we show that given an arbitrarily initial condition, the solution approaches a step function and hence develops a steep transition layer (interface) within a very short time. Because of the nonlocal term, some PDE tools such as comparison principle cannot be applied so that we have to introduce new method to overcome these diculties. Furthermore, in some cases, we obtain a sharp estimate for the thickness of interface. This is joint work with Danielle Hilhorst, Hiroshi Matano and Hendrik Weber.
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