Speaker: Hans Engler, Mathematics, Georgetown University

Title: On second order differential equations with asymptotically small dissipation

Abstract: The talk is concerned with the asymptotic properties for large times of solutions of the differential equation x''(t) + a(t)x'(t) + g(x(t)) = 0, t> 0 in a Hilbert space, where g(x) is the gradient of a suitable potential G(x) and the coefficient function a(t) is positive and decreases to zero. The problem occurs in stochastic approximation algorithms, and the equation also governs radial solutions of certain nonlinear elliptic systems. The talk will be concerned with necessary and sufficient conditions for the convergence of a natural energy function and of trajectories, for the case of convex as well as non-convex G(x). In the one-dimensional setting, a fairly complete description will be given for general smooth non-convex G. This is joint work with Alexandre Cabot (Montpellier, France) and Sebastien Gadat (Toulouse, France).

Time: Friday, Feb. 13, 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