PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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Title:Motion by Mean Curvature in Heterogeneous Medium
Seminar:Applied Analysis Seminar
Speaker:Aaron Yip, Purdue University
Abstract:
The talk will discuss some mathematical questions motivated by the motion of materials phase boundaries in heterogeneous medium. The ultimate goal is to derive effective, homogenized equation and study the property of the solution in large space-time regime. Motion by mean curvature is used as an illustrative example. It already involves interesting mathematical analysis due to the nonlinear interaction between the curvature and the background heterogeneity. In this talk, we will concentrate on periodic background environment. For some linearized version of motion by mean curvature flow, we derive the scaling behavior for the averaged velocity in some pinning and de-pinning regime. For the fully nonlinear version, we prove the existence, uniqueness and stability of pulsating waves (above the pinning threshold) for any normal direction. Furthermore, the effective speed of propagation is a Lipschitz continuous function of the normal. Connection with homogenization will be discussed. (This talk is based on joint works with Nicolas Dirr and Georgia Karali.)

Room Reservation Information

Room Number:MB106
Date:11 / 27 / 2007
Time:04:00pm - 05:00pm