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Applicable Analysis
An International Journal
Volume 85, 2006 - Issue 12
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Original Articles

Individual homogenization of nonlinear parabolic operators

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Pages 1433-1457 | Received 28 Aug 2006, Accepted 05 Oct 2006, Published online: 11 Dec 2006

References

  • Bensoussan , A , Lions , J-L and Papanicolaou , G . 1978 . Asymptotic Analysis for Periodic Structures , Amsterdam : North Holland .
  • Braides , A , Chiadò Piat , V and Defranceschi , A . 1992 . Homogenization of almost periodic monotone operators . Annales de l'Institute Henri Poincare. Analyse Non Linéaire , 9 : 399 – 432 .
  • Braides , A and Defranceschi , A . 1998 . Homogenization of Multiple Integrals , New York : Clarendon Press, Oxford University Press .
  • Bruno , G , Pankov , A and Pankova , T . 2000 . Time averaging for random nonlinear abstract parabolic equations . Abstract and Applied Analysis , 5 : 1 – 11 .
  • Chiadò Piat , V , Dal Maso , G and Defranceschi , A . 1990 . G-convergence of monotone operators . Annales de l;Institute Henri Poincare. Analyse Non Linéaire , 7 : 123 – 160 .
  • Cioranescu , D and Donato , P . 1999 . An Introduction to Homogenization , New York : Clarendon Press, Oxford University Press .
  • Dal Maso , G . 1993 . An Introduction to Γ-convergence , Boston : Birkhäuser .
  • Efendiev , Y and Pankov , A . 2003 . Numerical homogenization of monotone elliptic operators, . SIAM Multiscale Modeling Simulation , 1 : 62 – 79 .
  • Efendiev , Y and Pankov , A . 2004 . Numerical homogenization of nonlinear random parabolic operators . SIAM Multiscale Modeling Simulation , 2 : 237 – 268 .
  • Efendiev , Y and Pankov , A . 2004 . Numerical homogenization and correctors for nonlinear elliptic equations . SIAM Journal of Applied Mathematics , 65 : 43 – 68 .
  • Efendiev , Y and Pankov , A . 2005 . Homogenization of nonlinear random parabolic operators . Advance in Differential Equations , 10 ( 11 ) : 1235 – 1260 .
  • Fusco , N and Moscariello , G . 1986 . Further results on the homogenization of quasilinear operators . Ricerche Matematica , 35 : 231 – 246 .
  • Fusco , N and Moscariello , G . 1987 . On the homogenization of quasilinear divergence structure operators . Annali di Matematica Pura ed Applicata , 146 : 1 – 13 .
  • Gröger , K . 1989 . A W 1, p -estimate for solutions to mixed boundary value problems for second order elliptic differential equations . Mathematische Annalen , 283 : 679 – 687 .
  • Jikov , VV , Kozlov , SM and Oleinik , OA . 1994 . Homogenization of Differential Operators and Integral Functionals , New York : Springer-Verlag .
  • Lions , JL . 1969 . “ Quelques Méthodes de Résoluton des Problèmes aux Limites Non Linéairies ” . Paris : Dunod .
  • Pankov , A . 1984 . Homogenization and G-convergence of nonlinear elliptic operators in divergence form . Doklady Akademii Nauk SSSR (in Russian) , 278 : 37 – 41 .
  • Pankov , A . 1990 . Bounded and Almost periodic Solutions of Nonlinear Operator Differential Equations , Dordrecht : Kluwer .
  • Pankov , A . 1997 . “ Strong G-convergence of nonlinear elliptic operators and homogenization ” . In Constanin Carathéodory — An International Tribute , Edited by: Rassias , Th . 1075 – 1099 . Singapore : World Scientific Publishing .
  • Pankov , A . 1997 . G-convergence and Homogenization of Nonlinear Partial Differential Operators , Dordrecht : Kluwer Academic Publishers .
  • Showalter , RE . 1997 . Monotone Operators in Banach Space and Nonlinear Partial Differential Equations , Providence, RI : American Mathematical Society . Vol. 49 of Mathematical Surveys and Monographs
  • Svanstedt , N . 2000 . Correctors for the homogenization of monotone parabolic operators . Journal of Nonlinear Mathematical Physics , 7 : 268 – 283 .
  • Zhikov , VV , Kozlov , SM and Ole[ibreve]nik , OA . 1982 . Averaging of parabolic operators . Trudy Moskovskogo Matematicheskogo Obshchehestra , 45 : 182 – 236 . (in Russian)
  • Zhikov , VV , Kozlov , SM and Ole[ibreve]nik , OA . 1982 . Averaging of parabolic operators with almost periodic coefficients . Matematicheski Sbornik (N.S.) , 117 ( 159 ) : 69 – 85 . (in Russian)

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