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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 11
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Original Articles

Asymptotic heat equation for crossing superconductive thin walls

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Pages 2029-2043 | Received 04 Jun 2010, Accepted 06 May 2011, Published online: 09 Jun 2011

References

  • D. Cioranescu and F. Murat, Un terme étrange venu d'ailleurs, I and II, Nonlinear Partial Differential Equations and their Applications, College de France Seminar, Vols. II and III, Paris, 1979/1980 and 1980/1981; Research Notes in Mathematics, Vols. 60 and 70, Pitman, London, 1982 and 1983, pp. 98–138 and pp. 154–178.
  • Casado-Diaz , J . 2000 . Two-scale convergence for nonlinear Dirichlet problems in perforated domains . Proc. R. Soc. Edinburgh , 130 A : 249 – 276 .
  • Allaire , G . 1991 . Homogenization of the Navier–Stokes equations in open sets perforated with tiny holes. I. Abstract framewok, a volume distribution of holes . Arch. Rational. Mech. Anal. , 113 : 209 – 259 .
  • Damlamian , A and Donato , P . 1991 . Homogenization with small inclusions of increasingly complicated shapes . SIAM J. Math. Anal. , 22 ( 3 ) : 639 – 652 .
  • Mosco , U . 1994 . Composite media and asymptotic Dirichlets forms . J. Funct. Anal. , 123 : 368 – 421 .
  • Briane , M and Tchou , N . 2001 . Fibered microstructure for some non-local Dirichlet forms . Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 30 : 681 – 712 .
  • Bellieud , M and Bouchitté , G . 1998 . Homogenization of elliptic problems in a fiber reinforced structure. Non-local effects . Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 26 ( 3 ) : 407 – 436 .
  • Bellieud , M and Gruais , I . 2005 . Homogenization of an elastic material reinforced by very stiff or heavy fibers. Non-local effects. Memory effects . J. Math. Pures Appl. , 84 ( 1 ) : 55 – 96 .
  • Bellieud , M . 2005 . Homogenization of evolution problems for a composite medium with very small and heavy inclusions . ESAIM Control Optim. Calc. Var. , 11 ( 2 ) : 266 – 284 .
  • Bentalha , F , Gruais , I and Polisevski , D . 2006 . Homogenization of a conductive suspension in a Stokes–Boussinesq flow . Applicable Analysis , 85 ( 6–7 ) : 811 – 830 .
  • Bentalha , F , Gruais , I and Polisevski , D . 2007 . Diffusion process in a rarefied binary structure . Revue Roum. Math. Pures Appl. , 52 ( 2 ) : 129 – 149 .
  • Murat , F and Tartar , L . 1985 . “ Calcul des variations et homogénéisation ” . In Homogenization Methods: Theory and Applications in Physics , Edited by: Bergman , D , Lions , JL , Papanicolaou , G , Murat , F , Tartar , L and Sanchez-Palencia , E . Vol. 57 , 319 – 370 . Eyrolles, Paris : Collection de la Direction des Études et Recherches d'Électricité de France .
  • Héron , B , Mossino , J and Picard , C . 1994 . Homogenization of some quasilinear problems for stratified media with low and high conductivities . Differ. Integral Eqns. , 7 ( 1 ) : 157 – 178 .
  • Bouchitté , G and Picard , C . 1996 . Singular perturbations and homogenization in stratified media . Appl. Anal. , 61 ( 3–4 ) : 307 – 341 .
  • Bakhvalov , NS and Panasenko , GP . 1989 . “ Homogenization: Averaging Processes in Periodic Media ” . In Mathematical Application (Sov. Series) , Vol. 36 , Dordrecht : Kluwer Academic Publishers Group .
  • Cioranescu , D and Saint-Jean-Paulin , J . 1999 . Homogenization of Reticulated Structures , New York : Springer-Verlag .
  • Zhikov , VV and Pastukhova , SE . 2006 . Derivation of the limit equations of elasticity theory of thin sets . J. Math. Sci. , 135 ( 1 ) : 2637 – 2665 .
  • Bentalha , F , Gruais , I and Polisevski , D . 2008 . Diffusion in a highly rarefied binary structure of general periodic shape . Appl. Anal. , 87 ( 6 ) : 635 – 655 .
  • Gruais , I and Polisevski , D . 2007 . Homogenizing a critical binary structure of finite diffusivities . Asymptot. Anal. , 55 ( 1 ) : 85 – 102 .
  • Gruais , I and Polisevski , D . 2010 . ϵ-Periodic structures containing highly conductive thin layers . Rev. Roum. de Math. Pures Appl. , 55 ( 6 ) : 381 – 399 .
  • Gruais , I and Polisevski , D . 2010 . Homogenizing media containing a highly conductive honeycomb substructure . Asymptot. Anal. , 67 ( 1–2 ) : 33 – 43 .

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