| Autor: |
Wehbe, Ali, Koumaiha, Marwa, Toufaily, Layla |
| Předmět: |
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| Zdroj: |
Discrete & Continuous Dynamical Systems - Series S; May2022, Vol. 15 Issue 5, p1269-1305, 37p |
| Abstrakt: |
In this paper, we study the exact controllability of a system of two wave equations coupled by velocities with boundary control acted on only one equation. In the first part of this paper, we consider the -d case. Then, using a multiplier technique, we prove that, by observing only one component of the associated homogeneous system, one can get back a full energy of both components in the case where the waves propagate with equal speeds (i.e. in (1)) and where the coupling parameter is small enough. This leads, by the Hilbert Uniqueness Method, to the exact controllability of our system in any dimension space. It seems that the conditions and small enough are technical for the multiplier method. The natural question is then : what happens if one of the two conditions is not satisfied? This consists the aim of the second part of this paper. Indeed, we consider the exact controllability of a system of two one-dimensional wave equations coupled by velocities with a boundary control acted on only one equation. Using a spectral approach, we establish different types of observability inequalities which depend on the algebraic nature of the coupling parameter and on the arithmetic property of the wave propagation speeds. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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