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Controllability of the Wave Equation Governed by Mobile Point Controls

In: Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations

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  • Alexander Y. Khapalov

    (Washington State University, Department of Mathematics and Statistics)

Abstract

This chapter continues the discussion of Chap. 9 , dealing with the observability issues for the general hyperbolic equations equipped with the mobile degenerate sensors. We will now focus on the dual controllability issues for the wave equation governed by the mobile point actuators. In particular, we will show that the approximate controllability of this equation is possible in H D −[n∕2]−1(Ω) × H D −[n∕2]−2(Ω), while the exact controllability can hold in L 2(Ω) × H −1(Ω), provided that the control curves are carefully selected and that the control functions lie in [L ∞ (0, T; R n+1)] ′ .

Suggested Citation

  • Alexander Y. Khapalov, 2017. "Controllability of the Wave Equation Governed by Mobile Point Controls," Springer Books, in: Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations, chapter 0, pages 163-182, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60414-5_10
    DOI: 10.1007/978-3-319-60414-5_10
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