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Eighth Mississippi State - UAB Conference on Differential Equations & Computational Simulations
May 7-9, 2009
Department of Mathematics and Statistics, Mississippi State University
Mississippi State, MS, USA

Organizers
Mississippi State University & University of Alabama - Birmingham

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Singularities of complex solutions of Burgers equation
by
Peter Polacik
University of Minnesota
Coauthors: Vladimir Sverak

We consider the one-dimensional viscous Burgers equation allowing the unknown function to take complex values. We show that some solutions develop singularities in finite time. We then address several questions concerning the structure of the singularities and the behavior of the solutions near their singularities. Via Cole-Hopf transformation we translate these problems to questions about zeros of complex-valued solutions of the heat equation. While the problems remain interesting and nontrivial, they can be tackled with rather elementary tools.

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Date received: March 30, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxp-98.