Title: Parabolic Equations in Musielak-Orlicz-Sobolev Spaces
Author(s): M.L. Ahmed Oubeid, A. Benkirane, M. Sidi El Vally
Pages: 174-191
Cite as:
M.L. Ahmed Oubeid, A. Benkirane, M. Sidi El Vally, Parabolic Equations in Musielak-Orlicz-Sobolev Spaces, Int. J. Anal. Appl., 4 (2) (2014), 174-191.

Abstract


We prove in this paper the existence of solutions of nonlinear parabolic problems in Musielak-Orlicz-Sobolev spaces. An approximation and a trace results in inhomogeneous Musielak-Orlicz-Sobolev spaces have also been provided.

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References


  1. M.L.Ahmed Oubeid,A. Benkirane and M. Ould Mohamedhen val; Nonlinear elliptic equations involiving measur data in Musielak-Orlicz-Sobolev spaces, J.A. Diff. Eq and App Volume 4, Number 1, pp. 43-57 (2013)

  2. A. Benkirane and M. Ould Mohamedhen val; An existence result for nonlinear elliptic equations in Musielak-Orlicz-Sobolev spaces, Bull. Belg. Math. Soc. Simon Stevin Volume 20, Number 1 (2013), 57-75.

  3. A. Benkirane, J. Douieb, M. Ould Mohamedhen val; An approximation theorem in MusielakOrlicz-Sobolev spaces, Comment. Math. (Prace Matem.) Vol. 51, No. 1 (2011), 109-120.

  4. A. Benkirane and M. Ould Mohamedhen val; Some approximation properties in MusielakOrlicz-Sobolev spaces, Thai.J. Math. Vol. 10, No. 2 (2012), 371-381.

  5. A. Benkirane and M. Ould Mohamedhen val; Variational inequalities in Musielak-OrliczSobolev spaces, to appear in Bull. Belg. Math. Soc. Simon Stevin.

  6. L. Boccardo and F. Murat; Strongly nonlinear Cauchy problems with gradient dependent lower order nonlinearity, Pitman Research Notes in Mathematics 208 (Pitman, 1989) 247-254.

  7. L. Boccardo and F. Murat; Almost everywhere convergence of the gradients, Nonlinear Anal. 19 (1992) 581-597.

  8. H.Brzis; Analyse fonctionnelle,thorie et applications,3rd end, (Masson, Paris,1992).

  9. H.Brzis and F.E.Browder; Strongly nonlinear parabolic initial boundary value problems, Proc.Nat.Acad.Sci.U.S.A.76(1979)38-40.

  10. T.Donaldson; Inhomogeneous Orlicz-Sobolev spaces and nonlinrar parabolic initial boundary value problems, J.Differential Equations 16(1974)201-256.

  11. A.Elmahi; Strongly nonlinear parabolic initial-boundary value problems in Orlicz spaces,Electron. J. Differential Equations.09 (2002) 203-220.

  12. A.Elmahi, D.Meskine; Parabolic equations in orlicz spaces,J.London Math.Soc.72 (2)(2005) 410-428

  13. J.P. Gossez, Somme approximation properties in Orlicz Sobolev spaces, Studia Math. 74 (1982), 17-24.

  14. R.Landes and V.Mustonen, On the existence of weak solutions for quasilinear parabolic initial-boundary value problems , Proc.Roy.Soc. Edinburgh Sect. A 89 (1981), 217-237.

  15. R.Landes and V.Mustonen, A strongly nonlinear parabolic initial-boundary value problem, Ark. Mat. 25 (1987), 29-40.

  16. J.L.Lions; Quelques mthodes de rsolution des problmes aux limites non linaires ;(GauthiersVillars,1969).

  17. J. Musielak; Modular spaces and Orlicz spaces ;Lecture Notes in Math. 1034 (1983).

  18. J. Robert; Inequations variationnelles paraboliques fortement non lineaires ;(GauthiersVillars,1969).