Applied Mathematics and Optimization

, Volume 23, Issue 1, pp 109–154

Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems

  • I. Lasiecka
  • R. Triggiani
Article

DOI: 10.1007/BF01442394

Cite this article as:
Lasiecka, I. & Triggiani, R. Appl Math Optim (1991) 23: 109. doi:10.1007/BF01442394

Abstract

This paper studies (global) exact controllability of abstract semilinear equations. Applications include boundary control problems for wave and plate equations on the explicitly identified spaces of exact controllability of the corresponding linear systems.

Contents. 1. Motivating examples, corresponding results, literature. 1.1. Motivating examples and corresponding results. 1.2. Literature. 2. Abstract formulation. Statement of main result. Proof. 2.1. Abstract formulation. Exact controllability problem. 2.2. Assumptions and statement of main result. 2.3. Proof of Theorem 2.1. 3. Application: a semilinear wave equation with Dirichlet boundary control. Problem (1.1). 3.1. The caseγ = 1 in Theorem 1.1 for problem (1.1). 3.2. The caseγ = 0 in Theorem 1.1 for problem (1.1). 4. Application: a semilinear Euler—Bernoulli equation with boundary controls. Problem (1.14). 4.1. Verification of assumption (C.1): exact controllability of the linear system. 4.2. Abstract setting for problem (1.14). 4.3. Verification of assumptions (A.1)–(A.5). 4.4. Verification of assumption (C.2). 5. Proof of Theorem 1.2 and of Remark 1.2. Appendix A: Proof of Theorem 3.1. Appendix B: Proof of (4.9) and of (4.10b). References.

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • I. Lasiecka
    • 1
  • R. Triggiani
    • 1
  1. 1.Department of Applied MathematicsUniversity of VirginiaCharlottesvilleUSA

Personalised recommendations