Averaged null controllability for some hyperbolic equations depending on a parameter. (English) Zbl 1458.35251
Summary: The aim of this paper is to prove the averaged null controllability property for a wave equation with an unknown velocity of propagation parameter and for parameter-dependent vibrating plate equation under the effect of a boundary control. The choice of the Hilbert uniqueness method seems to be the best-adapted method to our theory, where the key point to prove the desired result is an averaged inverse inequality (averaged observability inequality). Consequently, we’ll prove the desired property for a large time enough and we’ll design a single control chosen independently of the parameter value transferring the average of the state to the origin.
MSC:
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 93B05 | Controllability |
| 74K20 | Plates |
Keywords:
Hilbert uniqueness method; parameter-dependent vibrating plate equation; averaged inverse inequalityReferences:
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