Applied Computational Mathematics Division


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PDEs from Monge-Kantorovich Mass Transportation Theory

Luca Petrelli
Mount St. Mary's University, Department of Mathematics and Computer Science

Wednesday, May 11, 2005 15:00-16:00,
NIST North (820), Room 145
Gaithersburg
Wednesday, May 11, 2005 13:00-14:00,
Room 4550
Boulder

Abstract: In this talk we will introduce the Monge-Kantorovich mass transportation problem and give a brief history of its solution. We will then briefly introduce gradient flows and show how PDEs can be recovered using results from the Monge-Kantorovich problem. We will discuss a few examples and then present some results on very general diffusion equations obtained with Adrian Tudorascu at Carnegie Mellon University. We will conclude by presenting some recent work on the subject, discussing the main advantages of the technique, and presenting some still open numerical and theoretical problems.

Speaker Bio: Dr. Luca Petrelli received his PhD in Mathematics from Carnegie Mellon University in 2004. After coming to the US from the University of Rome in 1998, he worked with David Kinderlehrer on the Wasserstein Metric problem. Further research included an examination of optimal transportation problems under this metric as well as general diffusion PDEs. Dr. Petrelli is currently an Assistant Professor at Mount St. Mary's University in Emmitsburg, Maryland.

Presentation Slides: PDF

Contact: P. M. Ketcham

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.