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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.

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
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