Continuous Observability of Hyperbolic Equations under Degenerate Sensors

Alexander Y. Khapalov
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Alexander Y. Khapalov: Washington State University, Department of Mathematics and Statistics

Chapter Chapter 9 in Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations, 2017, pp 147-162 from Springer

Abstract: 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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-60414-5_9

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DOI: 10.1007/978-3-319-60414-5_9

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