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Second Order Differential Equations with Asymptotically Small Dissipation
by
Hans Engler
Georgetown University
Coauthors: Alexandre Cabot, Sebastien Gadat
The time-asymptotic behavior of solutions for ordinary differential equations
x''(t) + a(t)x'(t) + g(x(t)) = 0
in a Hilbert space is discussed, where g is the gradient of a coercive potential G and a(t) is positive and vanishes at infinity. Results on the existence and non-existence of limits are given in the case of non-convex potentials with many stationary points. In the scalar case, a complete characterization of the behavior is given under generic assumptions. The equation occurs in optimization and governs radial solutions of semilinear elliptic problems.
Date received: September 10, 2007
Copyright © 2007 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 # cavp-08.