Exact Controllability of Semilinear Evolution Systems and Its Application
- X. Zhang
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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.
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- Exact Controllability of Semilinear Evolution Systems and Its Application
Journal of Optimization Theory and Applications
Volume 107, Issue 2 , pp 415-432
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- Kluwer Academic Publishers-Plenum Publishers
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- exact controllability
- semilinear systems
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- X. Zhang (1) (2)
- Author Affiliations
- 1. Institute of Mathematics, Fudan University, Shanghai, China
- 2. School of Mathematics, Sichuan University, Chengdu, China