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Continuous Observability of Hyperbolic Equations under Degenerate Sensors

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

In this chapter we intend to extend our studies of the observability properties of partial differential equations to a large class of linear second-order partial differential equations (PDEs) of hyperbolic type in n spatial dimensions. We will show that both the L ∞ (0, T; R n+1)- and C([0, T[; R n+1)-continuous observability properties are possible for these equations, provided that the observation data are supplied by finitely many, carefully selected, mobile degenerate sensors. We will consider both the point and spatially averaged sensors.

Suggested Citation

  • Alexander Y. Khapalov, 2017. "Continuous Observability of Hyperbolic Equations under Degenerate Sensors," Springer Books, in: Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations, chapter 0, pages 147-162, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60414-5_9
    DOI: 10.1007/978-3-319-60414-5_9
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