Journal of Optimization Theory and Applications

, Volume 107, Issue 2, pp 415–432

Exact Controllability of Semilinear Evolution Systems and Its Application

  • X. Zhang
Article

DOI: 10.1023/A:1026460831701

Cite this article as:
Zhang, X. Journal of Optimization Theory and Applications (2000) 107: 415. doi:10.1023/A:1026460831701

Abstract

In this paper, we obtain several abstract results concerning the exact controllability of semilinear evolution systems. First, we prove the null local exact controllability of semilinear first-order systems by means of the contraction mapping principle; in this case, we do not assume any compactness. Next, we derive the global and/or local exact controllability of semilinear second-order systems by means of the Schauder fixed-point theorem; in this case, we assume only the embedding of the related spaces having some compactness, which is reasonable for many concrete problems. Our main result shows that the observability of the dual of the linearized system implies the exact controllability of the original semilinear system. Finally, we apply our abstract results to the exact controllability of the semilinear wave equation.

exact controllabilitysemilinear systemsobservabilityinequalities

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • X. Zhang
    • 1
    • 2
  1. 1.Institute of MathematicsFudan UniversityShanghaiChina
  2. 2.School of MathematicsSichuan UniversityChengduChina