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Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation

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  • We study a damped semi-linear wave equation in a bounded domain of $\mathbb{R}^3$ with smooth boundary. It is proved that any $H^2$-smooth solution can be stabilised locally by a finite-dimensional feedback control supported by a given open subset satisfying a geometric condition. The proof is based on an investigation of the linearised equation, for which we construct a stabilising control satisfying the required properties. We next prove that the same control stabilises locally the non-linear problem.
    Mathematics Subject Classification: Primary: 35L71, 93B52; Secondary: 93B07.

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