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All issues Volume 55 / No 4 (July-August 2021) ESAIM: M2AN, 55 4 (2021) 1545-1568 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 4, July-August 2021
Page(s) 1545 - 1568
DOI https://doi.org/10.1051/m2an/2021028
Published online 29 July 2021
  1. A. Alphonse, M. Hintermüller and C.N. Rautenberg, Stability of the solution set of quasi-variational inequalities and optimal control. SIAM J. Control Optim. 58 (2020) 3508–3532. [CrossRef] [Google Scholar]
  2. J. Aponte, H.C. Abache, A. Sa-Neto and M. Octavio, Temperature dependence of the critical current in high-Tc superconductors. Phys. Rev. B 39 (1989) 2233–2237. [CrossRef] [Google Scholar]
  3. J.W. Barrett and L. Prigozhin, A quasi-variational inequality problem in superconductivity. Math. Models Methods Appl. Sci. 20 (2010) 679–706. [CrossRef] [Google Scholar]
  4. J.W. Barrett and L. Prigozhin, Sandpiles and superconductors: nonconforming linear finite element approximations for mixed formulations of quasi-variational inequalities. IMA J. Numer. Anal. 35 (2015) 1–38. [CrossRef] [Google Scholar]
  5. C.P. Bean, Magnetization of hard superconductors. Phys. Rev. Lett. 8 (1962) 250–253. [CrossRef] [Google Scholar]
  6. C.P. Bean, Magnetization of high-field superconductors. Rev. Mod. Phys. 36 (1964) 31–39. [CrossRef] [Google Scholar]
  7. M. Ciszek, B.A. Glowacki, S.P. Ashworth, A.M. Campbell, W.Y. Liang, R. Flükiger and R.E. Gladyshevskii, AC losses and critical currents in Ag/(Tl, Pb, Bi)-1223 tape. Phys. C: Supercond. Appl. 260 (1996) 93–102. [CrossRef] [Google Scholar]
  8. J.R. Clem, B. Bumble, S.I. Raider, W.J. Gallagher and Y.C. Shih, Ambegaokar-Baratoff–Ginzburg-Landau crossover effects on the critical current density of granular superconductors. Phys. Rev. B 35 (1987) 6637–6642. [CrossRef] [Google Scholar]
  9. G. Deutscher and K.A. Müller, Origin of superconductive glassy state and extrinsic critical currents in high-tc oxides. Phys. Rev. Lett. 59 (1987) 1745–1747. [CrossRef] [PubMed] [Google Scholar]
  10. K.-J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, with contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. Schnaubelt. In: Vol. 194 of Graduate Texts in Mathematics. Springer-Verlag, New York (2000). [Google Scholar]
  11. V. Girault and P. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, Berlin (1986). [Google Scholar]
  12. F. Jochmann, Well-posedness for Bean’s critical state model with displacement current. J. Math. Anal. Appl. 362 (2010) 505–513. [CrossRef] [Google Scholar]
  13. Y.B. Kim, C.F. Hempstead and A.R. Strnad, Magnetization and critical supercurrents. Phys. Rev. 129 (1963) 528–535. [CrossRef] [Google Scholar]
  14. A. Laurain, M. Winckler and I. Yousept, Shape optimization for superconductors governed by H(curl)-elliptic variational inequalities. SIAM J. Control Optim. 59 (2021) 2247–2272. [CrossRef] [Google Scholar]
  15. J.-L. Lions and G. Stampacchia, Variational inequalities. Comm. Pure Appl. Math. 20 (1967) 493–519. [CrossRef] [MathSciNet] [Google Scholar]
  16. F. Miranda, J.-F. Rodrigues and L. Santos, Evolutionary quasi-variational and variational inequalities with constraints on the derivatives. Adv. Nonlinear Anal. 9 (2020) 250–277. [CrossRef] [Google Scholar]
  17. S. Nicaise and F. Tröltzsch, A coupled Maxwell integrodifferential model for magnetization processes. Math. Nachr. 287 (2014) 432–452. [CrossRef] [Google Scholar]
  18. S. Nicaise and F. Tröltzsch, Optimal control of some quasilinear Maxwell equations of parabolic type. Discrete Contin. Dyn. Syst. Ser. S 10 (2017) 1375–1391. [Google Scholar]
  19. R. Picard, An elementary proof for a compact imbedding result in generalized electromagnetic theory. Math. Z. 187 (1984) 151–164. [CrossRef] [Google Scholar]
  20. L. Prigozhin, On the Bean critical-state model in superconductivity. Eur. J. Appl. Math. 7 (1996) 237–247. [CrossRef] [Google Scholar]
  21. J.F. Rodrigues and L. Santos, A parabolic quasi-variational inequality arising in a superconductivity model. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 29 (2000) 153–169. [Google Scholar]
  22. J.F. Rodrigues and L. Santos, Quasivariational solutions for first order quasilinear equations with gradient constraint. Arch. Ration. Mech. Anal. 205 (2012) 493–514. [CrossRef] [Google Scholar]
  23. W. Rudin, Functional analysis, 2nd edition. International Series in Pure and Applied Mathematics. McGraw-Hill Inc, New York (1991). [Google Scholar]
  24. F. Tröltzsch and A. Valli, Optimal control of low-frequency electromagnetic fields in multiply connected conductors. Optimization 65 (2016) 1651–1673. [CrossRef] [Google Scholar]
  25. F. Tröltzsch and A. Valli, Optimal voltage control of non-stationary eddy current problems. Math. Control Relat. Fields 8 (2018) 35–56. [CrossRef] [Google Scholar]
  26. N. Weck, Maxwell’s boundary value problem on Riemannian manifolds with nonsmooth boundaries. J. Math. Anal. Appl. 46 (1974) 410–437. [CrossRef] [Google Scholar]
  27. M. Winckler and I. Yousept, Fully discrete scheme for Bean’s critical-state model with temperature effects in superconductivity. SIAM J. Numer. Anal. 57 (2019) 2685–2706. [CrossRef] [Google Scholar]
  28. M. Winckler, I. Yousept and J. Zou, Adaptive edge element approximation for H(curl) elliptic variational inequalities of second kind. SIAM J. Numer. Anal. 58 (2020) 1941–1964. [CrossRef] [Google Scholar]
  29. I. Yousept, Optimal control of quasilinear H(curl)-elliptic partial differential equations in magnetostatic field problems. SIAM J. Control Optim. 51 (2013) 3624–3651. [Google Scholar]
  30. I. Yousept, Hyperbolic Maxwell variational inequalities for Bean’s critical-state model in Type-II superconductivity. SIAM J. Numer. Anal. 55 (2017) 2444–2464. [CrossRef] [Google Scholar]
  31. I. Yousept, Optimal control of non-smooth hyperbolic evolution maxwell equations in type-II superconductivity. SIAM J. Control Optim. 55 (2017) 2305–2332. [CrossRef] [Google Scholar]
  32. I. Yousept, Hyperbolic Maxwell variational inequalities of the second kind. ESAIM: COCV 26 (2020) 34. [CrossRef] [EDP Sciences] [Google Scholar]
  33. I. Yousept, Well-posedness theory for electromagnetic obstacle problems. J. Differ. Equ. 269 (2020) 8855–8881. [CrossRef] [Google Scholar]

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