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6th International Conference on Differential Equations and Dynamical Systems
May 22-26, 2008

Baltimore, Maryland, USA

Organizers
Xinzhi Liu, University of Waterloo; Gaston M. N'Guerekata, Morgan State University

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Free Boundary Problems for Darcy Flows
by
David Ambrose
Clemson University

I will present recent results on well-posedness of free surface problems in fluid flows, where the fluid velocities satisfy Darcy's Law. In both two and three dimensions, we find that the initial value problem is well-posed as long as a stability condition is satisfied; this is the nonlinear version of a condition of Saffman and Taylor. If time allows I will present further results, from joint work with Steve Shkoller, on well-posedness and stability conditions for some rotational Darcy flows.

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Date received: January 28, 2008

Copyright © 2008 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 # cavk-90.