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Graduate Seminar

Matteo Rinaldi
Carnegie Mellon University
Title: Introduction to Slow phase boundary motion in one space dimension

Abstract: We will be talking about a paper written by Lia Bronsard and Robert Kohn, where the limiting behavior of solutions of \[ u_t - \epsilon^2 u_{xx} + u^3 - u = 0 \] is studied. The analysis is based on "energy methods" and the initial data is assumed to have a "transition layer structure", i.e., it is close to a piecewise constant function with values +1 or -1 in some sense. The authors show that, as $\epsilon \to 0$, the transition points move slower than any power of $\epsilon$. Physical motivations for the study of such a model will be briefly discussed as well.

Date: Tuesday, October 21, 2014
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Zilin Jiang