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)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1978
Accession Number
ADA054547

Entities

People

  • A. Pazy

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Concrete
  • Continuity
  • Convergence
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Functional Analysis
  • Hilbert Space
  • Mathematics
  • North Carolina
  • Partial Differential Equations
  • Perturbations
  • Sequences
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space