Speaker: Dr. Jean-Philippe Lessard, Rutgers University and IAS

Title: A priori estimates and validated continuation for equilibria of high dimensional PDEs

Abstract: In this talk, I will introduce the validated continuation technique to the context of equilibria of partial differential equations defined on high dimensional spatial domains. For that effect, I will an> general a priori analytic estimates. These estimates are valid for any dimension and are used, together with rigorous computations, to construct a finite number of radii polynomials. These polynomials provide a computationally efficient method to prove, via a contraction argument, the existence and local uniqueness of solutions for a rather large class of nonlinear problems. We apply this technique to prove existence and local uniqueness of equilibrium solutions for the Cahn-Hilliard and the Swift-Hohenberg equations defined on two- and three-dimensional spatial domains. This is join work with Marcio Gameiro from Kyoto University.

Time: Friday, Nov. 20, 2009, 1:30-2:30 p.m.

Place: Science and Tech I, Room 242

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491