Controllability of an elliptic equation and its finite difference approximation by the shape of the domain

Numerische Mathematik

Volumn 95, Issue 1, 2003, Pages 63-99

  Chenais, D ^a   Zuazua, Enrique ^b  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041411651     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-002-0443-8     Document Type: Article

References (25)

1. M. Asch, G. Lebeau: Geometrical aspects of exact boundary controllability of the wave equation. A numerical study. ESAIM:COCV, 3, 163-212 (1998)
2. R. Abraham, J.E. Marsden, T. Ratiu: Manifolds, Tensor Analysis, and Applications, Addison-Wesley Publishing Company, 1983
3. C. Castro, E. Zuazua: Low frequency asymptotic analysis of a string with rapidly oscillating density, SIAM J. Appl. Math. 60, 1205-1233 (2000)
4. J. Céa: Optimization of distributed parameter structures, NATO Advanced Study Institutes series, 50, Haug E. & Céa J. Editors, Sijthoff and Noordhoff, 1981
5. D. Chenais: On the existence of a solution in a domain identification problem, Journal of Math. Analysis and Applications, 52(2), 189-219 (1975)
6. D. Chenais: Sur une famille de variétés à bord lipschitziennes. Application à un problème d'identification de domaines, Annales de l'Institut Fourier, XXVII(4), 201-231 (1977)
7. C. Fabre, J.P. Fuel, E. Zuazua: Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinburgh, 125 A, 31-61 (1995)
8. J. Hadamard: Mémoire sur le problème d'analyse relatif à l'équilibre des plaques élastiques encastrées, Mémoire des savants étrangers, (33), 1908
9. L. Hörmander: Linear Partial Differential equations, Springer Verlag, 1969
10. A. Iserles: A First Course on Numerical Analysis of Differential equations, Cambridge Texts in Applied Mathematics, Cambridge University Press, 1996
11. J.-L. Lions: Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués. Tomes 1 & 2. Masson, RMA 8 & 9, Paris, 1988
12. A. Lopez, E. Zuazua: Some new results related to the null controllability of the 1 - d heat equation, Seminaire X-EDP, Ecole Polytechnique, 1997-1998, VIII 1-22
13. F. Murat, J. Simon: Sur le contrôle par un domaine géométrique, Publication du laboratoire d'analyse numérique de l'Université Paris VI, 1976
14. J.H. Ortega: Comportamiento asintótico, control y estabilización de algunos sistemas parabólicos y de placas, PhD. Thesis, Universidad Complutense de Madrid, 1997
15. A. Osses, J.P. Puel: On the Controllability of the Stationary Stokes System with Linear Convection observed on an Interior Curve, Journal of Optimization Theory and Applications, 99(1), 201-234 (1998)
16. A. Osses, J.P. Puel: On the controllability of the Laplace equation observed on an interior curve, Rev. Matemática Complutense, 11(2), 403-441 (1998)
17. B. Rousselet: Optimization of distributed parameter structures, NATO Advanced Study Institutes series, 50, Haug E. & Céa J. Editors, Sijthoff and Noordhoff, 1474-1501 (1981)
18. B. Rousselet: Shape design sensitivity of a membrane, Journal of Optimization Theory and Applications, 40(4), 595-623 (1983)
19. J. Simon: Diferenciación con respecto al dominio. Lecture Notes, Universidad de Sevilla, 1989
20. J. Simon: Differentiation with respect to the domain in boundary value problems. Numer. Func. Anal. Optim. 2, 649-687 (1980)
21. J.P. Zolesio: Optimization of distributed parameter structures, NATO Advanced Study Institutes series, 50, Haug E. & Céa J. Editors, Sijthoff and Noordhoff, 1089-1151(1981)
22. E. Zuazua: Some problems and results on the controllability of Partial Differential equations, Proceedings of the Second European Conference of Mathematics, Budapest, July 1996, Progress in Mathematics, 169, 1998, Birkhäuser Verlag Basel/Switzerland, pp. 276-311
23. E. Zuazua: Observability of 1 - d waves in heterogeneous and semi-discrete media, In: Advances in Structural Control, J. Rodellar et al. eds, CIMNE, Barcelona, 1999, pp. 1-30
24. E. Zuazua: Boundary observability for the finite-difference space semi-discretizations of the 2 - d wave equation in the square, J. Math. Pures Appl. 78, 523-563 (1999)
25. E. Zuazua: Controllability of Partial Differential equations and its Semi-Discrete Approximations, Discrete and Continuous Dynamical Systems, 8(2), 469-513 (2002)