LONG-TIME BEHAVIOR FOR SEMILINEAR DEGENERATE PARABOLIC EQUATIONS ON ℝN

Title & Authors
LONG-TIME BEHAVIOR FOR SEMILINEAR DEGENERATE PARABOLIC EQUATIONS ON ℝN
Cung, The Anh; Le, Thi Thuy;

Abstract
We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\small{\mathbb{R}^N}$: \frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)
Keywords
semilinear degenerate parabolic equation;weak solution;global attractor;non-compact case;tail estimates method;
Language
English
Cited by
References
1.
C. T. Anh, N. D. Binh, and L. T. Thuy, On the global attractors for a class of semilinear degenerate parabolic equations, Ann. Polon. Math. 98 (2010), no. 1, 71-89.

2.
C. T. Anh, N. D. Binh, and L. T. Thuy, Attractors for quasilinear parabolic equations involving weighted p-Laplacian operators, Vietnam J. Math. 38 (2010), no. 3, 261-280.

3.
C. T. Anh, N. M. Chuong, and T. D. Ke, Global attractor for the m-semiflow generated by a quasilinear degenerate parabolic equation, J. Math. Anal. Appl. 363 (2010), no. 2, 444-453.

4.
C. T. Anh and P. Q. Hung, Global existence and long-time behavior of solutions to a class of degenerate parabolic equations, Ann. Polon. Math. 93 (2008), no. 3, 217-230.

5.
C. T. Anh and T. D. Ke, Long-time behavior for quasilinear parabolic equations involving weighted p-Laplacian operators, Nonlinear Anal. 71 (2009), no. 10, 4415-4422.

6.
C. T. Anh and T. D. Ke, On quasilinear parabolic equations involving weighted p-Laplacian operators, Nonlinear Differential Equations Appl. 17 (2010), no. 2, 195-212.

7.
P. Caldiroli and R. Musina, On a variational degenerate elliptic problem, Nonlinear Differential Equations Appl. 7 (2000), no. 2, 187-199.

8.
V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, Amer. Math. Soc. Colloq. Publ., Vol. 49, Amer. Math. Soc., Providence, RI, 2002.

9.
R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. I: Physical origins and classical methods, Springer-Verlag, Berlin, 1985.

10.
N. I. Karachalios and N. B. Zographopoulos, Convergence towards attractors for a degenerate Ginzburg-Landau equation, Z. Angew. Math. Phys. 56 (2005), no. 1, 11-30.

11.
N. I. Karachalios and N. B. Zographopoulos, Global attractors and convergence to equilibrium for degenerate Ginzburg-Landau and parabolic equations, Nonlinear Anal. 63 (2005), 1749-1768.

12.
N. I. Karachalios and N. B. Zographopoulos, On the dynamics of a degenerate parabolic equation: Global bifurcation of stationary states and convergence, Calc. Var. Partial Differential Equations 25 (2006), no. 3, 361-393.

13.
J.-L. Lions, Quelques Methodes de Resolution des Problemes aux Limites Non Lineaires, Dunod, Paris, 1969.

14.
J. C. Robinson, Infinite-Dimensional Dynamical Systems, Cambridge University Press, Cambridge, 2001.

15.
R. Rosa, The global attractor for the 2D Navier-Stokes flow on some unbounded domains, Nonlinear Anal. 32 (1998), no. 1, 71-85.

16.
R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, 2nd edition, Philadelphia, 1995.

17.
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, 2nd edition, Springer-Verlag, 1997.

18.
B. Wang, Attractors for reaction-diffusion equations in unbounded domains, Physica D 179 (1999), no. 1, 41-52.