- Research Article
- Open Access
Parabolic inequalities with nonstandard growths and
data
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.
Keywords
Differential EquationPartial Differential EquationOrdinary Differential EquationFunctional EquationExistence Result
Authors’ Affiliations
(1)
LERMA, École Mohammadia d'Ingénieurs, Université Mahammed V-Agdal, Rabat-Agdal, Morocco
(2)
Faculté des Sciences Juridiques, Économiques et Sociales, Université Hassan 1er, Settat, Morocco
(3)
GAN, Département de Mathématiques et d'Informatiques, Faculté des Sciences, Université Mahammed V-Agdal, Rabat, Morocco
References
- Adams RA: Sobolev Spaces, Pure and Applied Mathematics. Volume 65. Academic Press, New York; 1975:xviii+268.Google Scholar
- 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
- 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
- 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 - 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
- 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
- Gossez J-P: Some approximation properties in Orlicz-Sobolev spaces. Studia Mathematica 1982,74(1):17-24.MathSciNetMATHGoogle Scholar
- 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
- 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
- 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
- Robert J: Inéquations variationnelles paraboliques fortement non linéaires. Journal de Mathématiques Pures et Appliquées. Neuvième Série 1974, 53: 299-320.MATHGoogle Scholar
- Rudd M: Nonlinear constrained evolution in Banach spaces, M.S. thesis. University of Utah, Utah; 2003.Google Scholar
- 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
- 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.
