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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. Barbu and D. Tiba, Boundary controllability for the coincidence set in the obstacle problem, SIAM J. Control & Optim., Sept. 1991.
H. Brezis and W. A. Strauss, Semilinear second order elliptic equations in L1, J. Math. Soc. Japan 25 (1973).
J. Haslinger and P. Neittaanmäki, Finite element approximation for optimal shape design: theory and applications, Wiley, Chichester, 1988.
J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, 1971.
J. L. Lions, Controllabilité exacte, perturbations et stabilisation de systèmes distribués, Masson, Paris, 1988.
J. L. Lions and E. Magenes, Problèmes aux limites non homogènes, vol. 1, Dunod, Paris, 1968.
R. Mäkinen, P. Neittaanmäki and D. Tiba, A boundary controllability approach in optimal design problems, Univ. of Jyväskylä, Dept. of Math., Preprint 112 (1990).
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.
O. Pironneau, Optimal shape design for elliptic systems, Springer-Verlag, Berlin, 1984.
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.
D. Tiba, Une approche par controllabilité frontière dans les problèmes de design optimal, C.R.A.S. Paris, t. 310, Série I (1990).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Basel AG
About this chapter
Cite this chapter
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
Download citation
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