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Parabolic inequalities with nonstandard growths and data

Boundary Value Problems volume 2006, Article number: 29286 (2006) Cite this article

Abstract

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

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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)90012-6

    Article  MathSciNet  MATH  Google 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/S0024610705006630

    Article  MathSciNet  MATH  Google 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.

    MathSciNet  MATH  Google 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.

    Article  MathSciNet  MATH  Google 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.

    Article  MathSciNet  MATH  Google Scholar 

  7. Gossez J-P: Some approximation properties in Orlicz-Sobolev spaces. Studia Mathematica 1982,74(1):17-24.

    MathSciNet  MATH  Google 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.

    Chapter  Google 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)90053-8

    Article  MathSciNet  MATH  Google 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/S0024610700001423

    Article  MathSciNet  MATH  Google Scholar 

  11. Robert J: Inéquations variationnelles paraboliques fortement non linéaires. Journal de Mathématiques Pures et Appliquées. Neuvième Série 1974, 53: 299-320.

    MATH  Google 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-z

    Article  MathSciNet  MATH  Google Scholar 

  14. Rudd M, Schmitt K: Variational inequalities of elliptic and parabolic type. Taiwanese Journal of Mathematics 2002,6(3):287-322.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. LERMA, École Mohammadia d'Ingénieurs, Université Mahammed V-Agdal, Avenue Ibn Sina, Rabat-Agdal, BP 765, Morocco

    R Aboulaich, B Achchab, D Meskine & A Souissi

  2. Faculté des Sciences Juridiques, Économiques et Sociales, Université Hassan 1er, Settat, BP 784, Morocco

    B Achchab

  3. GAN, Département de Mathématiques et d'Informatiques, Faculté des Sciences, Université Mahammed V-Agdal, Avenue Ibn Battouta, Rabat, BP 1014, Morocco

    D Meskine & A Souissi

Authors
  1. R Aboulaich
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  2. B Achchab
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  3. D Meskine
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  4. A Souissi
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Corresponding author

Correspondence to D Meskine.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Aboulaich, R., Achchab, B., Meskine, D. et al. Parabolic inequalities with nonstandard growths and data. Bound Value Probl 2006, 29286 (2006). https://doi.org/10.1155/BVP/2006/29286

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

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Existence Result