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Observabilité frontière de l’equation des ondes. (Boundary observability of the wave equation). (English) Zbl 0598.35060

We prove an observability result for the solutions of the wave equation in a bounded domain, vanishing on its boundary. We show that we can find a \(T>0\) such that the total energy of any solution can be bounded by a constant multiple of the integral over \(\Gamma_ 0\times [0,T]\) of the square of the normal derivative of the solution, where \(\Gamma_ 0\) is the subset of the boundary on which the normal vector points away from the origin.

MSC:

35L05 Wave equation
35B35 Stability in context of PDEs
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