Open Access
Int. J. Simul. Multidisci. Des. Optim.
Volume 8, 2017
Article Number A11
Number of page(s) 8
Published online 18 August 2017
  1. Astrita G, Marrucci G. 1974. Principles of non-Newtonian fluid mechanics. McGraw-Hill: New York. [Google Scholar]
  2. Acerbi E, Mingine G. 2002. Regularity results for stationary electrorheological fluids. Arch. Ration. Mech. Anal., 164, 213–259. [CrossRef] [MathSciNet] [Google Scholar]
  3. Acerbi E, Mingione G, Seregin GA. 2004. Regularity results for parabolic systems related to a class of non Newtonian fluids. Ann. Ins. H. Poincaré Anal. Non Linéaire, 21, 25–60. [Google Scholar]
  4. Antontsev SN, Shmarev SI. 2009. Anisotropic parabolic equations with variable nonlinearity. Publ. Mat., 53(2), 355–399. [CrossRef] [MathSciNet] [Google Scholar]
  5. Antontsev SN, Shmarev SI. 2005. A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions. Nonlinear Anal., 60, 515–545. [CrossRef] [MathSciNet] [Google Scholar]
  6. Antontsev SN, Shmarev SI. 2009. Localization of solutions of anisotropic parabolic equations. Nonlinear Anal., 71, 725–737. [CrossRef] [Google Scholar]
  7. El Ouardi H, de Thelin F. 1989. Supersolutions and stabilization of the solutions of a nonlinear parabolic system. Publicacions Mathematiques, 33, 369–381. [CrossRef] [MathSciNet] [Google Scholar]
  8. El Ouardi H, El Hachimi A. 2002. Existence and regularity of a global attractor for doubly nonlinear parabolic equations. Electron. J. Diff. Eqns., 2002(45), 1–15. [Google Scholar]
  9. El Ouardi H, El Hachimi A. 2001. Existence and attractors of solutions for nonlinear parabolic systems. Electron. J. Qual. Theory Differ. Equ., 5, 1–16. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  10. El Ouardi H, El Hachimi A. 2006. Attractors for a class of doubly nonlinear parabolic systems. Electron. J. Qual. Theory Differ. Equ., 1, 1–15. [Google Scholar]
  11. El Ouardi H. 2011. Global attractor for quasilinear parabolic systems involving weighted p-Laplacian operators. J. Pure App. Mat. Advances App., 5(2), 79–97. [MathSciNet] [Google Scholar]
  12. El Ouardi H. 2013. Long-time behavior for a nonlinear parabolic systems with variable exponent of nonlinearity. Int. J. Adv. Math. Math. Sci., 2(1), 27–36. [Google Scholar]
  13. Esteban JR, Vazquez JL. 1982. On the equation of turbulent filtration in one-dimensional porous media. Nonlinear Anal., 10, 1303–1325. [CrossRef] [Google Scholar]
  14. Kristaly A, Radulescu V, Varga C. 2010. Variational principles in mathematical physics, geometry, and economics. Qualitative analysis of nonlinear equations and unilateral problems in Encyclopedia of mathematics and its applications, vol. 136. Cambridge University Press: Cambridge. [Google Scholar]
  15. Chang KC. 1986. Critical point theory and its applications. Shanghai Scientific and Technology Press: Shanghai. [Google Scholar]
  16. Fan X. 2007. Global C1,α regularity for variable exponent elliptic equations in divergence form. J. Diff. Equ., 235, 397–417. [CrossRef] [Google Scholar]
  17. Fan X, Zhao D. 2001. On the space Lp(x)(Ω) and Wm,p(x) (Ω). J. Math. Anal. Appl., 263, 749–760. [CrossRef] [Google Scholar]
  18. Fan X, Zhang QH. 2003. Existence of solutions for p(x)-Laplacian Dirichlet problem. Nonlinear Anal., 52, 1843–1852. [CrossRef] [MathSciNet] [Google Scholar]
  19. Lions JL. 1969. Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod: Paris. [Google Scholar]
  20. Lian S, Gao W, Yuan H, Cao C. 2012. Existence of solutions to an initial problem of evolutional p(x)-Laplace equations. Ann. I. H. Poincaré – AN, 29(3), 377–399, DOI: 10.1016/j.anihpc.2012.01.001. [CrossRef] [MathSciNet] [Google Scholar]
  21. Martinson LK, Pavlov KB. 1971. Unsteady shear flows of a conducting fluid with a rheological power law. Magnitnaya Gidrodinamika, 2, 50–58. [Google Scholar]
  22. Ruzicka M. 2000. Electrorheological fluids: Modeling and mathematical theory. Lecture Notes in Mathematics. vol. 1748. Berlin: Springer-Verlag. [CrossRef] [Google Scholar]
  23. Simon J. 1987. Compact sets in Lp(0, T; B). Ann. Mat. Pura Appl., 146, 65–96. [Google Scholar]
  24. Tedeev AF. 2007. The interface blow-up phenomenon and local estimates for doubly degenerate parabolic equation. Appl. Anal., 86(6), 755. [CrossRef] [MathSciNet] [Google Scholar]
  25. Zhao JN. 1993. Existence and nonexistence of solutions for ut = div(|∇u|p − 2u) + f(∇u, u, x, t). J. Math. Anal. Appl., 172(1), 130–146. [CrossRef] [MathSciNet] [Google Scholar]
  26. Fu Y, Zhang X. 2009. Multiple solutions for a class of p(x)-Laplacian systems. J. Inequal. Appl. Art., 2009(191649), 1–12. [Google Scholar]
  27. El Hamidi A. 2004. Existence results to elliptic systems with non standard growth condition. J. Math. Anal. Appl., 300, 30–42. [CrossRef] [MathSciNet] [Google Scholar]
  28. Marion M. 1987. Attractors for reaction-diffusion equation: existence and estimate of their dimension. Appl. Anal., 25, 101–147. [CrossRef] [MathSciNet] [Google Scholar]
  29. Ogras S, Mashiyev A, Avci M, Yucedag Z. 2008. Existence of solution for a class of elliptic systems in RN involving the (p(x), q(x))-Laplacian. J. Inequal. Appl., 612938, 16. [MathSciNet] [Google Scholar]
  30. Xu X, An Y. 2008. Existence and multiplicity of solutions for elliptic systems with nonstandard growth conditions in RN. Nonlinear Anal., 68, 956–968. [CrossRef] [MathSciNet] [Google Scholar]
  31. Wei Y, Gao W. 2007. Existence and uniqueness of local solutions to a class of quasilinear degenerate parabolic systems. Appl. Math. Comput., 190, 1250–1257. [CrossRef] [MathSciNet] [Google Scholar]
  32. Niu W. 2012. Long-time behavior for a nonlinear parabolic problem with variable exponents. J. Math. Anal. Appl., 393, 56–65. [CrossRef] [MathSciNet] [Google Scholar]

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