 99452 Th. Gallay, S. Slijepcevic
 Energy Flow in Extended Gradient Partial Differential Equations
(118K, (uuencoded gzipped) Postscript)
Nov 30, 99

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. As an example of an extended, formally gradient dynamical system, we
consider a damped hyperbolic equation in R^N with a locally Lipschitz
nonlinearity. Using local energy estimates, we study the semiflow defined
by this equation in the uniformly local energy space. If N <= 2, we show
in particular that there exist no periodic orbits, except for equilibria,
and we give a lower bound on the time needed for a bounded trajectory to
return in a small neighborhood of the initial point. We also prove that any
nonequilibrium point has a neighborhood which is never visited on average
by the trajectories of the system, and we deduce that the only uniformly
recurrent points are equilibria. Counterexamples are given which show that
these results cannot be extended to higher space dimensions.
 Files:
99452.src(
desc ,
99452.uu )