DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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