University of Minnesota Math Club

Math Club meetings will start for Fall 2015 on September 17. Please join us for seminars and lectures at 12:20 on Thursdays in Vincent Hall 570, and join our Facebook group, UMN Math Club! All majors are welcome to join and attend.

Date: October 8, 2015
12:20 pm
Vincent Hall 570

Title: On the Optimal Control of the Multiphase Stefan Problem.
Speaker: Bruno Poggi

Abstract: We consider the inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary heat flux is the control, and optimality criteria consists of the minimization of the $L_2$-norm declination of the trace of the solution to the Stefan problem from the temperature measurement on the fixed right boundary. State vector solves multiphase Stefan problem in a weak formulation, which is equivalent to Neumann problem for the quasilinear parabolic PDE with discontinuous coefficient. Full discretization through finite differences is implemented and discrete optimal control problem is introduced. We prove well-posedness in Sobolev spaces framework and convergence of discrete optimal control problems to the original problem both with respect to cost functional and control. Along the way the convergence of the method of finite differences for the weak solution of the multiphase Stefan problem is proved. The proof is based on achieving a uniform $L_{\infty}$ bound, and $W_2^{1,1}$-energy estimate for the discrete multiphase Stefan problem.
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The Math Club meets most Thursdays of the semester at 12:20 pm in Vincent 570.

The Math Club is open to all undergraduate students in mathematics; students from other programs are also welcome. The goal of the club is to provide a forum for students to meet and discuss issues of common interest, such as careers in mathematics, research, graduate school, academic concerns, internship opportunities, scholarships, special lectures and summer programs.

The Math Club is very grateful to Professor Willard and Mrs. Jane Miller for their generous donations to promote student activities.

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