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# Global exact controllability of semilinear wave equations by a double compactness/uniqueness argument

• We prove exact controllability in the energy space of semilinear wave equations with $L_2$-Neumann boundary controls. The present proof integrates a double compactness/uniqueness PDE-based argument in establishing the uniform continuous observability inequality of the linearized, dual, uncontrolled problem with the abstract operator-theoretic approach proposed in [11], [21]. The latter approach analyzes suitable families of collectively compact operators [1] and ultimately culminates with the application of a global inversion theorem (homeomorphism) [4], [17] to the original controlled semilinear problem.
Mathematics Subject Classification: Primary: 35; Secondary: 93.

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