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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 $\bbfR^3$. 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:
35B37PDE in connection with control problems (MSC2000)
35L35Higher order hyperbolic equations, boundary value problems
35L55Higher order hyperbolic systems
35L75Nonlinear hyperbolic PDE of higher $(>2)$ order
74K25Shells (solid mechanics)
49J20Optimal control problems with PDE (existence)
93B07Observability
49K10Free problems in several independent variables (optimality conditions)
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