Analysis of the HUM control operator and exact controllability for semilinear waves in uniform time

SIAM Journal on Control and Optimization

Volumn 48, Issue 2, 2009, Pages 521-550

  Dehman, B ^a   Lebeau, G ^b  

^a ENIT LAMSIN   (Tunisia)

^b UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

HUM control operator; Semilinear wave equation

Indexed keywords

CONTROLLABILITY; WAVE EQUATIONS;

BOUNDED DOMAINS; EXACT CONTROLLABILITIES; HUM CONTROL OPERATOR; LINEAR WAVES; NON-LINEAR WAVES; OPTIMAL CONTROLS; SEMILINEAR; SEMILINEAR WAVE EQUATION; STRICHARTZ INEQUALITIES;

MATHEMATICAL OPERATORS;

EID: 60649115669     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/070712067     Document Type: Article

References (20)

1. S. ALINHAC AND P. GÉRARD, Opérateurs pseudo-différentiels et théorème de Nash-Moser, Savoirs actuels, InterEditions, Paris, Editions du CNRS, Meudon, 1991.
2. C. BARDOS, G. LEBEAU, AND J. RAUCH, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), pp. 1024-1065.
3. N. BURQ AND P. GÉRARD, Condition nécessaire et suffisante pour la controlabilité exacte de l'équation des ondes, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), pp. 749-752.
4. N. BURQ, G. LEBEAU, AND F. PLANCHÓN, Global existence for energy critical waves in 3-D domains, J. Amer. Math. Soc, 21 (2008), pp. 831-845.
5. J.-Y. CHEMIN, Fluides parfaits incompressibles, Astérisque 209, SMF, Paris, 1995.
6. B. DEHMAN, G. LEBEAU, AND E. ZUAZUA, Stabilization and control for the suberitical semilinear wave equation, Ann. Sci. École Norm. Sup. (4), 36 (2003), pp. 525-551.
7. P. GÉRARD, Microlocal defect measures, Comm. Partial Differential Equations, 16 (1991), pp. 1762-1794.
8. P. GÉRARD, Oscillation and concentration effects in semilmear dispersive wave equations, J. Funct. Anal., 41 (1996), pp. 60-98.
9. J. GLNIBRE AND G. VELO, The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z., 189 (1985), pp. 487-505.
10. L. HÖRMANDER, Seminar, Lectures Notes at the Nordic Summer School of Mathematics, 1968.
11. L. HÖRMANDER, The Analysis of Linear Partial Differential Operators: Pseudodifferential Operators, III, Grundlehren Math. Wiss. 274, Springer-Verlag, Berlin, 1985.
12. L. KAPITANSKI, Weak and yet weaker solutions of semilinear wave equations, Comm. Partial Differential Equations, 19 (1994), pp. 1629-1676.
13. G. LEBEAU, Contrôle de l'équation de Schrödinger, J. Math. Pures Appl. (9), 71 (1992), pp. 267-291.
14. G. LEBEAU AND M. NODET, Experimental Study of the HUM Control Operator for Linear Waves, http://hal.inria.fr/ (2008).
15. J.-L. LIONS, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1, Rech. Math. Appl. 8, Masson, Paris, 1988.
16. Y. MEYER, Ondelettes et opérateurs, Actualités Math., Hermann, Paris, 1990.
17. D. L. RUSSELL, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., 20 (1978), pp. 639-739.
18. R. STRICHARTZ, Restriction of Fourier transform to quadratic surfaces and decay of solutions of the wave equation, Duke Math. J., 44 (1977), pp. 705-714.
19. E. ZLIAZUA, Exact controllability for the semilinear wave equation, J. Math. Pures Appl. (9), 69 (1990), pp. 1-31.
20. E. ZUAZUA, Exact controllability for semilinear wave equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 10 (1993), pp. 109-129.