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How to estimate observability constants of one-dimensional wave equations? Propagation versus spectral methods. (English) Zbl 1377.35185

The paper is devoted to providing explicit lower bounds of observability constants for one-dimensional wave equations with potential using two different methods: the first one uses a spectral decomposition of the solution of the equation, whereas the second one is based on a propagation argument along the characteristics. The structure of the paper is as follows. The main results of the paper are given in the first two sections. In Section 3, the authors present applications of results of Section 2 to control and stabilization of wave equations. Section 4 is devoted to the illustration of the main results of the paper, here the authors provide several numerical simulations to comment on both methods, illustrate and compare them.

MSC:

35L05 Wave equation
93B07 Observability
35Q93 PDEs in connection with control and optimization
35B35 Stability in context of PDEs
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References:

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