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The influence of magnetic steps on bulk superconductivity
1. | Lund University, Department of Mathematics, Box 118, SE-22100, Lund, Sweden |
2. | Lebanese University, Department of Mathematics, Hadath, Lebanon |
References:
[1] |
Y. Almog, B. Helffer and X. B. Pan, Mixed normal-superconducting states in the presence of strong electric currents, Arch. Rational Mech. Anal. (2016). doi:10.1007/s00205-016-1037-4 |
[2] |
K. Attar, The ground state energy of the two dimensional Ginzburg-Landau functional with variable magnetic field, Ann. I.H.Poincaré-AN, 32 (2015), 325-345.
doi: 10.1016/j.anihpc.2013.12.002. |
[3] |
K. Attar, Energy and vorticity of the Ginzburg-Landau model with variable magnetic field, Asympt. Anal., 93 (2015), 75-114.
doi: 10.3233/ASY-151286. |
[4] |
K. Attar, Pinning with a variable magnetic field of the two dimensional Ginzburg-Landau model, Non-Linear Analysis: TMA., 139 (2016), 1-54.
doi: 10.1016/j.na.2016.02.002. |
[5] |
V. Bonnaillie-Noël and S. Fournais, Superconductivity in domains with corners, Rev. Math. Phys., 19 (2007), 607-637.
doi: 10.1142/S0129055X07003061. |
[6] |
S. J. Chapman, Q. Du and M. D. Gunzburger, A Ginzburg-Landau type model of superconducting/normal junctions including Josephson junctions, European Journal of Applied Mathematics, 6 (1995), 97-114.
doi: 10.1017/S0956792500001716. |
[7] |
A. Contreras and X. Lamy, Persistence of superconductivity in thin shells beyond Hc1, Commun. Contemp. Math., 18 (2016),1550047, 21pp.
doi: 10.1142/S0219199715500479. |
[8] |
S. Fournais and B. Helffer, Spectral Methods in Surface Superconductivity, Progress in Nonlinear Differential Equations and their Applications. Vol. 77, Birkhäuser, Boston, 2010. |
[9] |
S. Fournais and A. Kachmar, The ground state energy of the three dimensional Ginzburg-Landau functional. Part I: Bulk regime, Commun. Part. Diff. Equations, 38 (2013), 339-383.
doi: 10.1080/03605302.2012.717156. |
[10] |
S. Fournais and A. Kachmar, Nucleation of bulk superconductivity close to critical magnetic field, Adv. Math., 226 (2011), 1213-1258.
doi: 10.1016/j.aim.2010.08.004. |
[11] |
S. Fournais and A. Kachmar, On the transition to the normal phase for superconductors surrounded by normal conductors, J. Differential Equations, 247 (2009), 1637-1672.
doi: 10.1016/j.jde.2009.04.012. |
[12] |
T. Giorgi and D. Phillips, The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model, SIAM J. Math. Anal., 30 (1999), 341-359.
doi: 10.1137/S0036141097323163. |
[13] |
B. Helffer and A. Mohamed, Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells, J. Funct. Anal., 138 (1996), 40-81.
doi: 10.1006/jfan.1996.0056. |
[14] |
B. Helffer and A. Kachmar, The ginzburg-landau functional with vanishing magnetic field, Arch. Rational Mech. Anal., 218 (2015), 55-122.
doi: 10.1007/s00205-015-0856-z. |
[15] |
P. D. Hislop, N. Popoff, N. Raymond and M. P. Sundqvist, Band functions in presence of magnetic steps, Mathematical Models and Methods in Applied Sciences, 26 (2016), 161-184.
doi: 10.1142/S0218202516500056. |
[16] |
A. Kachmar, The ground state energy of the three-dimensional Ginzburg-Landau model in the mixed phase, J. Funct. Anal., 261 (2011), 3328-3344.
doi: 10.1016/j.jfa.2011.08.002. |
[17] |
A. Kachmar, On the perfect superconducting solution for a generalized Ginzburg-Landau equation, Asymptot. Anal., 54 (2007), 125-164. |
[18] |
K. Lu and X. B. Pan, Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity, Physica D, 127 (1999), 73-104.
doi: 10.1016/S0167-2789(98)00246-2. |
[19] |
K. Lu and X. B. Pan, Surface nucleation of superconductivity in 3-dimension, J. Differential Equations, 168 (2000), 386-452.
doi: 10.1006/jdeq.2000.3892. |
[20] |
X. B. Pan and K. H. Kwek, Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains, Tran. Amer. Math. Soc., 354 (2002), 4201-4227.
doi: 10.1090/S0002-9947-02-03033-7. |
[21] |
R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, Vol. 343. American Mathematical Soc., 2001.
doi: 10.1090/chel/343. |
[22] |
E. Sandier and S. Serfaty, Vortices in the Magnetic Ginzburg-Landau Model, Progress in Nonlinear Partial Differential Equations and Their Applications. Vol. 70, Birkhäuser, 2007. |
[23] |
E. Sandier and S. Serfaty, The decrease of bulk superconductivity close to the second critical field in the Ginzburg-Landau model, SIAM J. Math. Anal., 34 (2003), 939-956.
doi: 10.1137/S0036141002406084. |
show all references
References:
[1] |
Y. Almog, B. Helffer and X. B. Pan, Mixed normal-superconducting states in the presence of strong electric currents, Arch. Rational Mech. Anal. (2016). doi:10.1007/s00205-016-1037-4 |
[2] |
K. Attar, The ground state energy of the two dimensional Ginzburg-Landau functional with variable magnetic field, Ann. I.H.Poincaré-AN, 32 (2015), 325-345.
doi: 10.1016/j.anihpc.2013.12.002. |
[3] |
K. Attar, Energy and vorticity of the Ginzburg-Landau model with variable magnetic field, Asympt. Anal., 93 (2015), 75-114.
doi: 10.3233/ASY-151286. |
[4] |
K. Attar, Pinning with a variable magnetic field of the two dimensional Ginzburg-Landau model, Non-Linear Analysis: TMA., 139 (2016), 1-54.
doi: 10.1016/j.na.2016.02.002. |
[5] |
V. Bonnaillie-Noël and S. Fournais, Superconductivity in domains with corners, Rev. Math. Phys., 19 (2007), 607-637.
doi: 10.1142/S0129055X07003061. |
[6] |
S. J. Chapman, Q. Du and M. D. Gunzburger, A Ginzburg-Landau type model of superconducting/normal junctions including Josephson junctions, European Journal of Applied Mathematics, 6 (1995), 97-114.
doi: 10.1017/S0956792500001716. |
[7] |
A. Contreras and X. Lamy, Persistence of superconductivity in thin shells beyond Hc1, Commun. Contemp. Math., 18 (2016),1550047, 21pp.
doi: 10.1142/S0219199715500479. |
[8] |
S. Fournais and B. Helffer, Spectral Methods in Surface Superconductivity, Progress in Nonlinear Differential Equations and their Applications. Vol. 77, Birkhäuser, Boston, 2010. |
[9] |
S. Fournais and A. Kachmar, The ground state energy of the three dimensional Ginzburg-Landau functional. Part I: Bulk regime, Commun. Part. Diff. Equations, 38 (2013), 339-383.
doi: 10.1080/03605302.2012.717156. |
[10] |
S. Fournais and A. Kachmar, Nucleation of bulk superconductivity close to critical magnetic field, Adv. Math., 226 (2011), 1213-1258.
doi: 10.1016/j.aim.2010.08.004. |
[11] |
S. Fournais and A. Kachmar, On the transition to the normal phase for superconductors surrounded by normal conductors, J. Differential Equations, 247 (2009), 1637-1672.
doi: 10.1016/j.jde.2009.04.012. |
[12] |
T. Giorgi and D. Phillips, The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model, SIAM J. Math. Anal., 30 (1999), 341-359.
doi: 10.1137/S0036141097323163. |
[13] |
B. Helffer and A. Mohamed, Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells, J. Funct. Anal., 138 (1996), 40-81.
doi: 10.1006/jfan.1996.0056. |
[14] |
B. Helffer and A. Kachmar, The ginzburg-landau functional with vanishing magnetic field, Arch. Rational Mech. Anal., 218 (2015), 55-122.
doi: 10.1007/s00205-015-0856-z. |
[15] |
P. D. Hislop, N. Popoff, N. Raymond and M. P. Sundqvist, Band functions in presence of magnetic steps, Mathematical Models and Methods in Applied Sciences, 26 (2016), 161-184.
doi: 10.1142/S0218202516500056. |
[16] |
A. Kachmar, The ground state energy of the three-dimensional Ginzburg-Landau model in the mixed phase, J. Funct. Anal., 261 (2011), 3328-3344.
doi: 10.1016/j.jfa.2011.08.002. |
[17] |
A. Kachmar, On the perfect superconducting solution for a generalized Ginzburg-Landau equation, Asymptot. Anal., 54 (2007), 125-164. |
[18] |
K. Lu and X. B. Pan, Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity, Physica D, 127 (1999), 73-104.
doi: 10.1016/S0167-2789(98)00246-2. |
[19] |
K. Lu and X. B. Pan, Surface nucleation of superconductivity in 3-dimension, J. Differential Equations, 168 (2000), 386-452.
doi: 10.1006/jdeq.2000.3892. |
[20] |
X. B. Pan and K. H. Kwek, Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains, Tran. Amer. Math. Soc., 354 (2002), 4201-4227.
doi: 10.1090/S0002-9947-02-03033-7. |
[21] |
R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, Vol. 343. American Mathematical Soc., 2001.
doi: 10.1090/chel/343. |
[22] |
E. Sandier and S. Serfaty, Vortices in the Magnetic Ginzburg-Landau Model, Progress in Nonlinear Partial Differential Equations and Their Applications. Vol. 70, Birkhäuser, 2007. |
[23] |
E. Sandier and S. Serfaty, The decrease of bulk superconductivity close to the second critical field in the Ginzburg-Landau model, SIAM J. Math. Anal., 34 (2003), 939-956.
doi: 10.1137/S0036141002406084. |
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