Free Access
Issue |
ESAIM: COCV
Volume 21, Number 2, April-June 2015
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Page(s) | 487 - 512 | |
DOI | https://doi.org/10.1051/cocv/2014035 | |
Published online | 09 March 2015 |
- M. Abramowitz and I.A. Stegun, Handbook of mathematical functions with formulas graphs and mathematical tables. Edited by Milton. New York, Dover (1972). [Google Scholar]
- F. Alabau-Boussouira, P. Cannarsa, and G. Fragnelli, Carleman estimates for degenerate parabolic operators with applications to null controllability. J. Evol. Equ. 6 (2006) 161–204. [CrossRef] [MathSciNet] [Google Scholar]
- S. Alinhac and C. Zuily, Uniqueness and nonuniqueness of the Cauchy problem for hyperbolic operators with double characteristics. Commun. Partial Differ. Equ. 6 (1981) 799–828. [CrossRef] [Google Scholar]
- Y. Almog, The stability of the normal state of superconductors in the presence of electric currents. Siam J. Math. Anal. 40 (2008) 824–850. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Almog and B. Helffer, Global stability of the normal state of superconductors in the presence of a strong electric current. Commun. Math. Phys. 330 (2014) 1021–1094. [CrossRef] [Google Scholar]
- Y. Almog, B. Helffer and X. Pan, Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field II: The large conductivity limit. SIAM J. Math. Anal. 44 (2012) 3671–3733. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Almog, B. Helffer and X. Pan, Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field. Trans. Amer. Math. Soc. 365 (2013) 1183–1217. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Almog, B. Helffer and X.-B. Pan, Superconductivity near the normal state under the action of electric currents and induced magnetic fields in R2. Commun. Math. Phys. 300 (2010) 147–184. [CrossRef] [Google Scholar]
- K. Beauchard, Null controllability of Kolmogorov-type equations. Math. Control Signals Syst. 26 (2014) 145–176. [CrossRef] [Google Scholar]
- K. Beauchard, P. Cannarsa and R. Guglielmi. Some controllability results for the 2D Grushin equations. J. Eur. Math. Soc. 16 (2014) 67–101. [CrossRef] [MathSciNet] [Google Scholar]
- J.-M. Bony, Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés. Ann. Inst. Fourier 19 (1969) 277–304. [CrossRef] [MathSciNet] [Google Scholar]
- H. Brézis, Analyse Fonctionnelle, Théorie et Applications. Masson, Paris (1983). [Google Scholar]
- J.-M. Buchot and J.-P. Raymond, Feedback stabilization of a boundary layer equation, part2: Nonhomogeneous state equations and numerical simulations. Appl. Math. Res. Express 2009 (2010) 877–122. [Google Scholar]
- J.-M. Buchot and J.-P. Raymond, Feedback stabilization of a boundary layer equation, part 1. ESAIM:COCV 17 (2011) 506–551. [CrossRef] [EDP Sciences] [Google Scholar]
- P. Cannarsa and L. de Teresa, Controllability of 1-D coupled degenerate parabolic equations. Electron. J. Differ. Equ. 73 (2009) 21. [Google Scholar]
- P. Cannarsa, G. Fragnelli and D. Rocchetti, Null controllability of degenerate parabolic operators with drift. Netw. Heterog. Media 2 (2007) 695–715. [CrossRef] [MathSciNet] [Google Scholar]
- P. Cannarsa, G. Fragnelli and D. Rocchetti, Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form. J. Evol. Equ. 8 (2008) 583–616. [CrossRef] [MathSciNet] [Google Scholar]
- P. Cannarsa, P. Martinez and J. Vancostenoble, Persistent regional null controllability for a class of degenerate parabolic equations. Commun. Pure Appl. Anal. 3 (2004) 607–635. [CrossRef] [MathSciNet] [Google Scholar]
- P. Cannarsa, P. Martinez and J. Vancostenoble, Null controllability of degenerate heat equations. Adv. Differ. Equ. 10 (2005) 153–190. [Google Scholar]
- P. Cannarsa, P. Martinez and J. Vancostenoble, Carleman estimates for a class of degenerate parabolic operators. SIAM J. Control Optim. 47 (2008) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
- P. Cannarsa, P. Martinez and J. Vancostenoble, Carleman estimates and null controllability for boundary-degenerate parabolic operators. C. R. Math. Acad. Sci. Paris 347 (2009) 147–152. [CrossRef] [MathSciNet] [Google Scholar]
- E.B. Davies, Wild spectral behaviour of anharmonic oscillators. Bull. London Math. Soc. 32 (2000) 432–438. [CrossRef] [MathSciNet] [Google Scholar]
- S. Didelot, Etude d’une perturbation singulière elliptique dégénérée. Thèse de doctorat, Reims (1999). [Google Scholar]
- H.O. Fattorini and D. Russel, Exact controllability theorems for linear parabolic equations in one space dimension. Arch. Ration. Mech. Anal. 43 (1971) 272–292. [Google Scholar]
- C. Flores and L. de Teresa, Carleman estimates for degenerate parabolic equations with first order terms and applications. C. R. Math. Acad. Sci. Paris 348 (2010) 391–396. [CrossRef] [MathSciNet] [Google Scholar]
- A.V. Fursikov and O.Y. Imanuvilov, Controllability of evolution equations. Vol. 34 of Lect. Notes Series. Seoul National University Research Institute of Mathematics Global Analysis Research Center, Seoul (1996). [Google Scholar]
- B. Helffer, Spectral Theory and its Applications. Cambridge University Press (2013). [Google Scholar]
- B. Helffer and D. Robert, Propriétés asymptotiques du spectre d’opérateurs pseudo-différentiels sur Rn. Commun. Partial Differ. Eq. 7 (1982) 795–882. [CrossRef] [Google Scholar]
- B. Helffer and J. Sjöstrand, From resolvent bounds to semigroup bounds, Appendix of a course by Sjöstrand. Proc. of the Evian Conference (2009). Preprint arXiv:1001.4171 [Google Scholar]
- R. Henry, On the semi-classical analysis of Schrödinger operators with purely imaginary electric potentials in a bounded domain. Preprint arXiv:1405.6183 [Google Scholar]
- O.Y. Imanuvilov, Boundary controllability of parabolic equations. Uspekhi. Mat. Nauk 48 (1993) 211–212. [Google Scholar]
- O.Y. Imanuvilov, Controllability of parabolic equations. Mat. Sb. 186 (1995) 109–132. [Google Scholar]
- T. Kato, Perturbation Theory for Linear operators. Springer-Verlag, Berlin New-York (1966). [Google Scholar]
- G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur. Commun. Partial Differ. Eq. 20 (1995) 335–356. [CrossRef] [Google Scholar]
- G. Lebeau and J. Le Rousseau, On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations. ESAIM:COCV 18 (2012) 712–747. [CrossRef] [EDP Sciences] [Google Scholar]
- P. Martinez and J. Vancostenoble, Carleman estimates for one-dimensional degenerate heat equations. J. Evol. Equ. 6 (2006) 325–362. [CrossRef] [MathSciNet] [Google Scholar]
- P. Martinez, J. Vancostonoble and J.-P. Raymond, Regional null controllability of a linearized Crocco type equation. SIAM J. Control Optim. 42 (2003) 709–728. [CrossRef] [MathSciNet] [Google Scholar]
- B.-T. Nguyen and D.S. Grebekov, Localization of laplacian eigenfunctions in circular and elliptical domains. SIAM J. Appl. Math. 73 780–803. [Google Scholar]
- O.A. Oleinik and V.N. Samokhin, Mathematical Models in Boundary Layer Theory. In vol. 15 of Appl. Math. Math. Comput. Chapman Hall CRC, Boca Raton, London, New York (1999). [Google Scholar]
- A. Pazy, Semigroups of linear operators and applications to partial differential equations. Appl. Math. Sci. Springer Verlag, New-York (1983). [Google Scholar]
- K. Pravda-Starov, A complete study of the pseudo-spectrum for the rotated harmonic oscillator. J. London Math. Soc. 73 (2006) 745–761. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Sibuya, Global theory of a second order linear ordinary differential equation with a polynomial coefficient. Amsterdam, North-Holland (1975). [Google Scholar]
- K.M. Siegel, An inequality involving Bessel functions of argument nearly equal to their orders. Proc. Amer. Math. Soc. 4 (1953) 858–859. [CrossRef] [MathSciNet] [Google Scholar]
- J. Toth and S. Zelditch, Counting nodal lines wich touch the boundary of an analytic domain. J. Differ. Geometry 81 (2009) 649–686. [Google Scholar]
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