Approximate controllability of linear parabolic equations in perforated domains

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 6, Issue , 2001, Pages 21-38

  Donato, Patrizia ^a,b   Nabil, Aïssam ^c  

^a UNIVERSITÉ DE ROUEN   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c IBN ZOHR UNIVERSITY   (Morocco)

Author keywords

Approximate controlability; Homogenization; Linear parabolic equation

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; INTEGRAL EQUATIONS; LINEAR EQUATIONS; MATRIX ALGEBRA; PARAMETER ESTIMATION; SET THEORY; THEOREM PROVING;

A PRIORITY ESTIMATION; APPROXIMATE CONTROLLABILITY; HOMOGENIZATION; LINEAR PARABOLIC EQUATIONS; PERFORATED DOMAINS;

CONTROLLABILITY;

EID: 0035696164     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2001102     Document Type: Article

References (14)

1. C. Brizzi and J.P. Chalot, Homogénéisation dans des ouverts à frontière fortement oscillante. Thèse a l’Université de Nice (1978).
2. D. Cioranescu and P. Donato, Exact internal controllability in perforated domains. J. Math. Pures Appl. 319 (1989) 185-213.
3. D. Cioranescu and P. Donato, An introduction to Homogenization. Oxford University Press (1999).
4. D. Cioranescu and J. Saint Jean Paulin, Homogenization in open sets with holes. J. Math. Anal. Appl. 319 (1979) 509-607.
5. R. Dautray and J.-L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et Techniques. Masson, Tome 3, Paris (1985).
6. E. De Giorgi, Sulla convergenza di alcune successioni di integrali del tipo dell’area. Rend. Mat. 4 (1975) 277-294.
7. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale. Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (8) 58 (1975) 842-850.
8. P. Donato and A. Nabil, Homogéneisation et controlabilite approchee de l’equation de la chaleur dans des domaines perfores. C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 789-794.
9. P. Donato and A. Nabil, Homogenization and correctors for heat equation in perforated domains. Ricerche di Matematica (to appear).
10. C. Fabre, J.P. Puel and E. Zuazua, Controlabilite approchee de l’equation de la chaleur semilineaire. C. R. Acad. Sci. Paris Sér. I Math. 314 (1992) 807-812.
11. C. Fabre, J.P. Puel and E. Zuazua, Approximate controllability for the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 31-61.
12. J.-L. Lions, Remarques sur la controlabilite approchee, in Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos, octubre 1990. Grupo de Analisis Matemético Aplicado de la University of Mélaga, Spain (1991) 77-87.
13. J.-C. Saut and B. Scheurer, Unique continuation for some evolution equations. J. Differential Equations 66 (1987) 118-139.
14. E. Zuazua, Approximate controllability for linear parabolic equations with rapidly oscillating coefficients. Control Cybernet. 23 (1994) 1-8.