Prevalent Behavior of Strongly Order Preserving Semiflows

Details Prevalent Behavior of Strongly Order Preserving Semiflows Prevalent Behavior of Strongly Order Preserving Semiflows

2006-05-08

arxiv.org/abs/math/0605202v1

Mathematics

Dynamical Systems

18 pages

Scientific paper

10.1007/s10884-007-9084-z

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results in terms of the measure-theoretic notion of prevalence. For monotone reaction-diffusion systems with Neumann boundary conditions on convex domains, we show that the set of continuous initial data corresponding to solutions that converge to a spatially homogeneous equilibrium is prevalent. We also extend a previous generic convergence result to allow its use on Sobolev spaces. Careful attention is given to the measurability of the various sets involved.

Affiliated with

Also associated with

No associations

Rating

Prevalent Behavior of Strongly Order Preserving Semiflows does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Prevalent Behavior of Strongly Order Preserving Semiflows, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Prevalent Behavior of Strongly Order Preserving Semiflows will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-463668