Open Access

Parabolic inequalities with nonstandard growths and data

Boundary Value Problems20062006:29286

https://doi.org/10.1155/BVP/2006/29286

Received: 25 July 2005

Accepted: 19 December 2005

Published: 7 June 2006

Abstract

We prove an existence result for solutions of nonlinear parabolic inequalities with data in Orlicz spaces.

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Authors’ Affiliations

(1)
LERMA, École Mohammadia d'Ingénieurs, Université Mahammed V-Agdal
(2)
Faculté des Sciences Juridiques, Économiques et Sociales, Université Hassan 1er
(3)
GAN, Département de Mathématiques et d'Informatiques, Faculté des Sciences, Université Mahammed V-Agdal

References

  1. Adams RA: Sobolev Spaces, Pure and Applied Mathematics. Volume 65. Academic Press, New York; 1975:xviii+268.Google Scholar
  2. Donaldson T: Inhomogeneous Orlicz-Sobolev spaces and nonlinear parabolic initial value problems. Journal of Differential Equations 1974,16(2):201-256. 10.1016/0022-0396(74)90012-6MathSciNetView ArticleMATHGoogle Scholar
  3. Elmahi A, Meskine D: Parabolic equations in Orlicz spaces. Journal of the London Mathematical Society. Second Series 2005,72(2):410-428. 10.1112/S0024610705006630MathSciNetView ArticleMATHGoogle Scholar
  4. Elmahi A, Meskine D:Strongly nonlinear parabolic equations with natural growth terms and data in Orlicz spaces. Portugaliae Mathematica. Nova Série 2005,62(2):143-183.MathSciNetMATHGoogle Scholar
  5. Elmahi A, Meskine D: Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces. Nonlinear Analysis. Theory, Methods & Applications 2005,60(1):1-35.MathSciNetView ArticleMATHGoogle Scholar
  6. Gossez J-P: Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients. Transactions of the American Mathematical Society 1974, 190: 163-205.MathSciNetView ArticleMATHGoogle Scholar
  7. Gossez J-P: Some approximation properties in Orlicz-Sobolev spaces. Studia Mathematica 1982,74(1):17-24.MathSciNetMATHGoogle Scholar
  8. Gossez J-P: A strongly nonlinear elliptic problem in Orlicz-Sobolev spaces. In Nonlinear Functional Analysis and Its Applications, Part 1 (Berkeley, Calif, 1983), Proc. Sympos. Pure Math.. Volume 45. American Mathematical Society, Rhode Island; 1986:455-462.View ArticleGoogle Scholar
  9. Gossez J-P, Mustonen V: Variational inequalities in Orlicz-Sobolev spaces. Nonlinear Analysis. Theory, Methods & Applications 1987,11(3):379-392. 10.1016/0362-546X(87)90053-8MathSciNetView ArticleMATHGoogle Scholar
  10. Le VK, Schmitt K: Quasilinear elliptic equations and inequalities with rapidly growing coefficients. Journal of the London Mathematical Society. Second Series 2000,62(3):852-872. 10.1112/S0024610700001423MathSciNetView ArticleMATHGoogle Scholar
  11. Robert J: Inéquations variationnelles paraboliques fortement non linéaires. Journal de Mathématiques Pures et Appliquées. Neuvième Série 1974, 53: 299-320.MATHGoogle Scholar
  12. Rudd M: Nonlinear constrained evolution in Banach spaces, M.S. thesis. University of Utah, Utah; 2003.Google Scholar
  13. Rudd M: Weak and strong solvability of parabolic variational inequalities in Banach spaces. Journal of Evolution Equations 2004,4(4):497-517. 10.1007/s00028-004-0153-zMathSciNetView ArticleMATHGoogle Scholar
  14. Rudd M, Schmitt K: Variational inequalities of elliptic and parabolic type. Taiwanese Journal of Mathematics 2002,6(3):287-322.MathSciNetMATHGoogle Scholar

Copyright

© Aboulaich et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.