Indirect internal controllability of weakly coupled degenerate wave equations. (English) Zbl 1495.35118
Authors’ abstract: This article is devoted to the study of the exact controllability for a system of weakly coupled one dimensional degenerate wave equations. An internal locally control acts on only one equation. We show that, when the coupling parameter which depends on the degree of degradation is sufficiently small, the observation of the velocity of the first component of the solution on a left neighborhood of \(x = 1\) allow us to get back a weakened energy of initial data of the second component of the solution for a sufficiently large time \(T\). Using the Hilbert Uniqueness Method, we then establish an indirect exact controllability result.
Reviewer: Kaïs Ammari (Monastir)
MSC:
| 35L52 | Initial value problems for second-order hyperbolic systems |
| 35L80 | Degenerate hyperbolic equations |
| 93B07 | Observability |
| 93C20 | Control/observation systems governed by partial differential equations |
Keywords:
internal locally observability; indirect controllability; degenerate wave equations; coupleReferences:
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