Abstract
The study of observability is the study of deducing information about the state of a dynamical system from incomplete measurements. Discrete observability asks if we can recover the initial data with only a discrete set of measurements. Discrete observability of the heat equation has been studied for bounded domains in Euclidean space and compact homogeneous spaces by Gilliam, Li and Martin [4], and Wallace and Wolf [6]. This paper examines discrete observability of the wave equation on bounded domains in Euclidean space. The solutions to the wave equation involve an additional initial condition, and the terms of the series solution no longer decay with time, so a new approach is needed.
This paper is based on a chapter in the author’s Ph.D. thesis, which was completed at Dartmouth College.
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References
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© 1993 Springer Science+Business Media New York
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DeStefano, A. (1993). Discrete Observability of the Wave Equation on Bounded Domains in Euclidean Space. In: Bowers, K., Lund, J. (eds) Computation and Control III. Progress in Systems and Control Theory, vol 15. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0321-6_9
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DOI: https://doi.org/10.1007/978-1-4612-0321-6_9
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