Uniqueness results for stokes equations and their consequences in linear and nonlinear control problems

Caroline Fabre

ESAIM: Control, Optimisation and Calculus of Variations (1996)

  • Volume: 1, page 267-302
  • ISSN: 1292-8119

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Fabre, Caroline. "Uniqueness results for stokes equations and their consequences in linear and nonlinear control problems." ESAIM: Control, Optimisation and Calculus of Variations 1 (1996): 267-302. <http://eudml.org/doc/90499>.

@article{Fabre1996,
author = {Fabre, Caroline},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Linear and nonlinear Stokes equations; controllability; uniqueness properties; Carleman estimates; approximate controllability; Navier-Stokes equations; linearized Stokes equation; fixed point theorem},
language = {eng},
pages = {267-302},
publisher = {EDP Sciences},
title = {Uniqueness results for stokes equations and their consequences in linear and nonlinear control problems},
url = {http://eudml.org/doc/90499},
volume = {1},
year = {1996},
}

TY - JOUR
AU - Fabre, Caroline
TI - Uniqueness results for stokes equations and their consequences in linear and nonlinear control problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1996
PB - EDP Sciences
VL - 1
SP - 267
EP - 302
LA - eng
KW - Linear and nonlinear Stokes equations; controllability; uniqueness properties; Carleman estimates; approximate controllability; Navier-Stokes equations; linearized Stokes equation; fixed point theorem
UR - http://eudml.org/doc/90499
ER -

References

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  1. [1] J.-M. Coron: On the controllability of 2-D incompressible Navier Stokes equations with the Navier slip boundary conditions, ESAIM: Control, Optimisation and Calculus of Variations, www.emath.fr/cocv/, 1, 1996, 35-75. Zbl0872.93040MR1393067
  2. [2] C. Fabre, J.-P. Puel and E. Zuazua: Approximate controllability of the semilinear heat equation, Proc. of the Royal Soc. of Edinburgh, 125A, 1995, 31-61. Zbl0818.93032MR1318622
  3. [3] C. Fabre and G. Lebeau: Prolongement unique des solutions de l'équation de Stokes, Comm. Part. Diff. Eq., 21, 1996, 573-596. Zbl0849.35098MR1387461
  4. [4] E. Fernandez-Cara and J. Real: On a conjecture due to J.-L. Lions, Non Linear Analysis, Theory, Methods and Applications, 1995. Zbl0844.35082
  5. [5] A. Fursikov et O. Imanuvilov: Controllability of evolution equations, Lecture note series 34, Res. Inst. Math, GARC, Seoul National University, 1996. Zbl0862.49004MR1406566
  6. [6] L. Hörmander: Linear Partial Differential Operators, Tome 3, Springer-Verlag, 1985. MR404822
  7. [7] G. Lebeau and L. Robbiano: Contrôle exact de l'équation de la chaleur, Comm. Part. Diff. Eq., 20, 1995, 335-356. Zbl0819.35071MR1312710
  8. [8] J.-L. Lions: Remarks on approximate controllability, J. Analyse Math., 59, 1992, 103-116. Zbl0806.35101MR1226954
  9. [9] X. Saint Raymond: Elementary introduction to the theory of pseudodifferentiel operators. Studies in advance math, 1991. Zbl0847.47035MR1211419
  10. [10] D. Robert: Autour de l'approximation semi-classique. Progress in Math. n° 68, Birkhauser, 1987. Zbl0621.35001MR897108
  11. [11] J.-C. Saut and B. Scheurer: Unique continuation for some evolution equations, Journal Differential Equations, 66, (1), 1987, 118-139. Zbl0631.35044MR871574
  12. [12] J.-C. Saut and R. Temam: Generic properties of Navier Stokes equations. Indiana Univ. Math. Journal 29, 1980, 427-445. Zbl0445.76023MR570691
  13. [13] L. Tartar: Topics in nonlinear analysis. Publications mathématiques d'Orsay, 78.13. Zbl0395.00008
  14. [14] E. Zuazua: Exact boundary controllability for the semilinear wave equation. Nonlinear differential equations and their applications, H. Brezis and J.-L. Lions Eds., Séminaire du Collège de France 1987-1988, vol X, Research Notes in Mathematics, Pitman, p. 357-391, 1991. Zbl0731.93011MR1131832
  15. [15] J.-L. Lions and E. Zuazua: A generic uniqueness result for the Stokes System and its control theoretical consequences. In the volume Partial Differential Equations and Applications, P. Marcellini, G. Talenti and E. Visentini eds., Marcel-Dekker Inc., LNPAS # 177, 221-235, 1996. Zbl0852.35112MR1371594

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