Control properties for second-order hyperbolic systems in anisotropic cases with applications in inhomogeneous and anisotropic elastodynamic systems. (English) Zbl 1406.35182
In the paper, the authors prove a control property for a second-order hyperbolic system in anisotropic and inhomogeneous cases with Dirichlet control. A system with variable coefficient matrices in a bounded domain in \(\mathbb{R}^n\) with \(C^2\)-boundary is considered. Using the Hilbert uniqueness method, the authors deduce the exact controllability of the corresponding control problem. The same results for linear elastodynamic systems are provided to illustrate the application of the results.
Reviewer: Vyacheslav I. Maksimov (Ekaterinburg)
MSC:
| 35L51 | Second-order hyperbolic systems |
| 74E05 | Inhomogeneity in solid mechanics |
| 74E10 | Anisotropy in solid mechanics |
| 93B05 | Controllability |
| 93B07 | Observability |
| 93B52 | Feedback control |
Keywords:
observability inequality; Dirichlet control; Hilbert uniqueness method; exact controllabilityReferences:
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