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Controllability-type properties for elliptic systems and applications

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Estimation and Control of Distributed Parameter Systems

Abstract

We consider approximate and exact controllability results for elliptic problems. These results enable one to formulate optimal shape design problems in a fixed domain with certain boundary conditions.

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References

  1. V. Barbu and D. Tiba, Boundary controllability for the coincidence set in the obstacle problem, SIAM J. Control & Optim., Sept. 1991.

    Google Scholar 

  2. H. Brezis and W. A. Strauss, Semilinear second order elliptic equations in L1, J. Math. Soc. Japan 25 (1973).

    Google Scholar 

  3. J. Haslinger and P. Neittaanmäki, Finite element approximation for optimal shape design: theory and applications, Wiley, Chichester, 1988.

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  4. J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, 1971.

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  5. J. L. Lions, Controllabilité exacte, perturbations et stabilisation de systèmes distribués, Masson, Paris, 1988.

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  6. J. L. Lions and E. Magenes, Problèmes aux limites non homogènes, vol. 1, Dunod, Paris, 1968.

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  7. R. Mäkinen, P. Neittaanmäki and D. Tiba, A boundary controllability approach in optimal design problems, Univ. of Jyväskylä, Dept. of Math., Preprint 112 (1990).

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  8. F. Murat and J. Simon, Etude de problémes d’optimal design, Optimization Techniques, Modelling and Optimization in the Service of Man, J. Cea (ed.), Lecture Notes in Computer Science 41, Springer-Verlag, Berlin, 1976, pp. 54–62.

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  9. O. Pironneau, Optimal shape design for elliptic systems, Springer-Verlag, Berlin, 1984.

    Book  Google Scholar 

  10. D. Tiba, R. Mäkinen, P. Neittaanmäki and T. Tiihonen, A boundary control approach to an optimal design problem, Control of distributed parameter systems, A. El Jai and M. Amouroux (eds.), Pergamon Press, 1990, pp. 415–418.

    Google Scholar 

  11. D. Tiba, Une approche par controllabilité frontière dans les problèmes de design optimal, C.R.A.S. Paris, t. 310, Série I (1990).

    Google Scholar 

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© 1991 Springer Basel AG

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Tiba, D., Neittaanmäki, P., Mäkinen, R. (1991). Controllability-type properties for elliptic systems and applications. In: Desch, W., Kappel, F., Kunisch, K. (eds) Estimation and Control of Distributed Parameter Systems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 100. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6418-3_24

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  • DOI: https://doi.org/10.1007/978-3-0348-6418-3_24

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-2676-0

  • Online ISBN: 978-3-0348-6418-3

  • eBook Packages: Springer Book Archive

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