Keywords:-

Keywords: p(x)-laplacian operator; Existence; Uniqueness; Variable exponents; Parabolic System; Asymptotic Behaviour.

Article Content:-

Abstract

This paper presents the existence and uniqueness of the initial and boundary value problem to a system of evolution (p1(x); p2(x))

References:-

References

G. Astrita, G. Marrucci : Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, 1974.

E. Acerbi, G. Mingine : Regularity results for stationary electrorheological uids, Arch. Ration.

Mech. Anal. (164) (2002); 213259.

E. Acerbi, G. Mingione, G.A. Seregin : Regularity results for parabolic systems related to a

class of non Newtonian uids. Ann. Ins. H. Poincaré Anal. Non Linéaire 21 (1) (2004), 25-60.

H. W. Alt, S. Luckhauss : Quasilinear elliptic and parabolic di¤erential equations. Math. Z,

(1983), 311-341.

S.N. Antontsev, S.I. Shmarev : Anisotropic parabolic equations with variable nonlinearity.

Publ. Mat. 53(2)(2009), 355399.

S.N. Antontsev, S.I. Shmarev : A model porous medium equation with variable exponent of

nonlinearity: existence, uniqueness and localization properties of solutions. Nonlinear Anal.

(2005), 515545.

S.N. Antontsev, S.I. Shmarev : Localization of solutions of anisotropic parabolic equations,

Nonlinear Anal. 71(2009), 725737.

L. Dung : Ultimate Boundedness of Solutions and Gradients of a class of Degenerate Parabolic

Systems. Nonlinear Analysis T.M.A, vol.39, (2000), 157171.

L. Dung : Global attractors and steady states for a class of reaction di¤usion systems. J.

Di¤erential equations, vol. 147, (1998), 129.

A. El Hamidi : Existence results to elliptic systems with non standard growth condition, J.

Math. Anal. Appl. 300 (2004) 3042.

H. EL Ouardi, F. de Thelin : Supersolutions and Stabilization of the Solutions of a Nonlinear

Parabolic System. Publicacions Mathematiques, vol 33 (1989), 369381.

H. El Ouardi, A. El Hachimi : Existence and Attractors of Solutions for Nonlinear Parabolic

Systems, EJQTDE, (2001), No. 5, 116.

H. El Ouardi, A. El Hachimi : Attractors for a class of doubly nonlinear parabolic systems, E.

J. Qualitative Theory of Di¤. Equ., No. 1. (2006), 115.

H. El Ouardi : On the Finite dimension of attractors of doubly nonlinear parabolic systems

with l-trajectories, Archivum Mathematicum (BRNO), Tomus 43 (2007), 289-303.

H. El Ouardi : Global attractor for quasilinear parabolic systems involving weighted p-

Laplacian operators, J. Pure and App. Mat. Advances and App. Vo(5) Num.2 (2011), 79-97.

J. R. Esteban, J. L. Vazquez : On the equation of turbulent lteration in one-dimensional

porous media, Nonlinear Anal. 10(1982), 13031325.G. Fragnelli : Positive periodic solutions for a system of anisotropic parabolic equations. J.

Math. Anal. Appl. 367 (2010), 204228.

Y. Fu, X. Zhang : Multiple solutions for a class of p(x)

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Ouardi, H. E. (2016). Existence, Uniqueness and Asymptotic Behaviour of Solutions for a class of Parabolic Systems involving (p1(x); p2(x)). International Journal Of Mathematics And Computer Research, 4(06), 1429-1440. Retrieved from https://ijmcr.in/index.php/ijmcr/article/view/51