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Uniform indirect boundary controllability of semi-discrete $ 1 $-$ d $ coupled wave equations

  • * Corresponding author: Abdeladim El Akri

    * Corresponding author: Abdeladim El Akri 

The first author would like to thank S. Micu for fruitful discussions on several parts of this paper during his visit to Craiova University

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  • In this paper, we treat the problem of uniform exact boundary controllability for the finite-difference space semi-discretization of the $ 1 $-$ d $ coupled wave equations with a control acting only in one equation. First, we show how, after filtering the high frequencies of the discrete initial data in an appropriate way, we can construct a sequence of uniformly (with respect to the mesh size) bounded controls. Thus, we prove that the weak limit of the aforementioned sequence is a control for the continuous system. The proof of our results is based on the moment method and on the construction of an explicit biorthogonal sequence.

    Mathematics Subject Classification: Primary: 93B05, 35L05, 30E05; Secondary: 65M06.


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