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


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 case γ = 1 in Theorem 1.1 for problem (1.1). 3.2. The case γ = 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. © 1991 Springer-Verlag New York Inc.

Publication Title

Applied Mathematics & Optimization