Strong Convergence of Semigroups of Nonlinear Contractions in Hilbert Space.
Abstract
The present paper deals with the strong convergence of trajectories S(t)x of a strongly continuous semigroup of contractions S(t), as t approaches infinity. A general sufficient condition for such convergence to occur is introduced and some examples in which the condition is satisfied are provided. Strengthening the general convergence condition, sufficient conditions for certain rates of convergence of S(t)x to its limit are exhibited. In particular a sufficient condition for a trajectory to reach equilibrium in finite time is given. The convergence as t approaches infinity of solutions of certain nonautonomous equations and a discrete version of all the previous results are briefly discussed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1978
- Accession Number
- ADA054547
Entities
People
- A. Pazy
Organizations
- University of Wisconsin–Madison