DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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