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**Observability inequalities for shallow shells.**
*(English)*
Zbl 0974.35013

The author established some observability inequalities from boundary for a general shallow shell with a middle surface of any shape. The middle surface is viewed as a Riemann manifold with the induced metric in \(\mathbb{R}^3\). With the assumption (H2) be established an estimate for the model proposed in the case that no boundary conditions are improved. Using all the above he established continuous observability estimates for two kinds of boundary conditions: Dirichlet and Neumann, which have a physical meaning with an explicit observability time and hence, by duality, exact controllability results.

Finally, several examples of the middle surface that verify the main assumption (H2) are considered.

Finally, several examples of the middle surface that verify the main assumption (H2) are considered.

Reviewer: Stefan Zanfir (Craiova)

### MSC:

35B37 | PDE in connection with control problems (MSC2000) |

35L35 | Initial-boundary value problems for higher-order hyperbolic equations |

35L55 | Higher-order hyperbolic systems |

35L75 | Higher-order nonlinear hyperbolic equations |

74K25 | Shells |

49J20 | Existence theories for optimal control problems involving partial differential equations |

93B07 | Observability |

49K10 | Optimality conditions for free problems in two or more independent variables |