On long-time behaviour of the positive solutions of nonhomogeneous non-Newtonian equation

References

• Esteban , JR and Vazquez , JR . 1988 . Homogeneous diffusion in R with power-like nonlinear diffusivity . Arch. Rational Mech. Anal. , 103 : 39 – 88 .
   Web of Science ®Google Scholar
• Ahmed , N and Sunada , DK . 1969 . Nonlinear flows in porous media . J. Hydraulics. Div. Proc. Amer. Soc. Civil Eng. , 95 : 1847 – 1857 .
   Google Scholar
• Tedeev , AF . 2004 . Conditions for the time global existence and nonexistence of a compact support of solutions to the Cauchy problem for quasilinear degenerate parabolic equations . Sib. Math. J. , 45 : 155 – 164 .
   Web of Science ®Google Scholar
• Babin , AV and Vishik , MI . 1992 . Attractors of Evolution Equations , Amsterdam : North-Holland .
   Google Scholar
• Eden , A , Michaux , B and Rakotoson , J-M . 1991 . Doubly nonlinear parabolic-type equations as dynamical systems . J. Dyn. Differ. Equ. , 3 : 87 – 131 .
   Google Scholar
• Eden , A and Rakotoson , J-M . 1994 . Exponential attractors for a doubly non-linear equation . J. Math. Anal. Appl. , 185 : 321 – 339 .
   Google Scholar
• El Hachimi , A and El Ouardi , H . 2002 . Existence and regularity of a global attractor for doubly non-linear parabolic equations . Electron. J. Differ. Equ. , 45 : 1 – 15 .
   Google Scholar
• Takeuchi , S and Yokota , T . 2003 . Global attractors for a class of degenerate diffusion equations . Electron. J. Differ. Equ. , 2003 : 1 – 13 .
   Google Scholar
• Gentile , CB and Primo , M . 2004 . Parameter dependent quasi-linear parabolic equations . Nonlinear Anal. , 59 : 801 – 812 .
   Google Scholar
• Babin , AV and Vishik , MI . 1990 . Attractors of differential evolution equations in unbounded domain . Proc. Roy. Soc. Edinburgh Sect. A , 116 : 221 – 243 .
   Google Scholar
• Feireisl , E , Laurencot , Ph , Simondon , F and Toure , H . 1994 . Compact attractors for reaction diffusion equations in Rn . C. R. Acad. Sci. Paris Sér I Math. , 319 : 147 – 151 .
   Google Scholar
• Feireisl , E , Laurençot , Ph and Simondon , F . 1995 . Compact attractors for degenerate parabolic equations in Rn . C. R. Acad. Sci. Paris Sér I Math. , 320 : 1079 – 1083 .
   Google Scholar
• Feireisl , E , Laurençot , Ph and Simondon , F . 1996 . Global attractors for degenerate parabolic equations on unbounded domains . J. Differ. Equ. , 129 : 239 – 261 .
   Google Scholar
• Khanmamedov , AKh . 2006 . Existence of a global attractor for the parabolic equation with nonlinear Laplacian principal part in an unbounded domain . J. Math. Anal. Appl. , 316 ( 2 ) : 601 – 615 .
   Web of Science ®Google Scholar
• Tsutsumi , M . 1988 . On solutions of some doubly nonlinear degenerate parabolic equations with absorption . JMMA , 132 : 187 – 212 .
   Google Scholar
• Lions , J-L . 1969 . Quelques methodes de resolution des problemes aux limites nonlineaires , Paris : Dunod, Gauthier Villars .
   Google Scholar
• Blanchard , D and Francfort , GA . 1988 . Study of double nonlinear heat equation with no growth assumptions on the parabolic term . SIAM J. Anal. Math. , 19 : 1032 – 1056 .
   Web of Science ®Google Scholar
• Temam , R . 1988 . Infinite Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematics Sciences, Vol. 68 , New York : Springer–Verlag .
   Google Scholar
• Zhong , CK , Yang , MH and Sun , CY . 2006 . The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction–diffusion equations . J. Differ. Equ. , 223 : 367 – 399 .
   Web of Science ®Google Scholar