科研之友
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摘要
We address the numerical approximation of boundary controls for systems of the form y%26quot;+ A(My) = 0 which models dynamical elastic shell structure. The membranal operator A(M) is self-adjoint and of mixed order, so that it possesses a non empty and bounded essential spectrum sigma(ess), (A(M)). Consequently, the exact controllability does not hold uniformly with respect to the initial data. Thus the numerical computation of controls by the way of dual approach and gradient method may fail, even if the initial data belongs to the orthogonal of the space spanned by the eigenfunctions associated with sigma(ess), (A(M)). In this work, we adapt a variational approach introduced in [Pablo Pedregal, Inverse Problems (26) 015004 (2010)] for the wave equation and obtain a robust method of approximation. This new approach does not require any information on the spectrum of the operator A(M). We also show that it allows to extract, from any initial data (y(0), y(1)), a controllable component for the mixed order system. We illustrate these properties with some numerical experiments. We also consider a relaxed controllability case for which uniform property holds.
- 出版日期2013-3
