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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 673605, 15 pages
Asymptotic Behavior of a Class of Degenerate Parabolic Equations
1School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Received 19 August 2012; Revised 19 November 2012; Accepted 23 November 2012
Academic Editor: Andrew Pickering
Copyright © 2012 Hongtao Li and Shan Ma. 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.
- J. W. Cholewa and T. Dlotko, Global Attractors in Abstract Parabolic Problems, vol. 278, Cambridge University Press, Cambridge, UK, 2000.
- A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, vol. 25, North-Holland Publishing, Amsterdam, The Netherland, 1992.
- M. Marion, “Attractors for reaction-diffusion equations: existence and estimate of their dimension,” Applicable Analysis, vol. 25, no. 1-2, pp. 101–147, 1987.
- M. Marion, “Approximate inertial manifolds for reaction-diffusion equations in high space dimension,” Journal of Dynamics and Differential Equations, vol. 1, no. 3, pp. 245–267, 1989.
- Q. Ma, S. Wang, and C. Zhong, “Necessary and sufficient conditions for the existence of global attractors for semigroups and applications,” Indiana University Mathematics Journal, vol. 51, no. 6, pp. 1541–1557, 2002.
- J. C. Robinson, Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, Cambridge University Press, Cambridge, UK, 2001.
- R. Temam, Infinite Dimensional Dynamical Dystems in Mechanics and Physics, vol. 68, Springer, Berlin, Germany, 2nd edition, 1997.
- J. Valero and A. Kapustyan, “On the connectedness and asymptotic behaviour of solutions of reaction-diffusion systems,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 614–633, 2006.
- C.-K. Zhong, M.-H. Yang, and C.-Y. Sun, “The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations,” Journal of Differential Equations, vol. 223, no. 2, pp. 367–399, 2006.
- R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Volume 1: Physical origins and classical methods, Springer, Berlin, Germany, 1990.
- N. I. Karachalios and N. B. Zographopoulos, “Convergence towards attractors for a degenerate Ginzburg-Landau equation,” Zeitschrift für Angewandte Mathematik und Physik, vol. 56, no. 1, pp. 11–30, 2005.
- N. I. Karachalios and N. B. Zographopoulos, “Global attractors and convergence to equilibrium for degenerate Ginzburg-Landau and parabolic equations,” Nonlinear Analysis: Theory, Methods and Applications, vol. 63, no. 5–7, pp. e1749–e1768, 2005.
- P. Caldiroli and R. Musina, “On a variational degenerate elliptic problem,” NoDEA Nonlinear Differential Equations and Applications, vol. 7, no. 2, pp. 187–199, 2000.
- C. T. Anh and P. Q. Hung, “Global attractors for a class of degenerate parabolic equations,” Acta Mathematica Vietnamica, vol. 34, no. 2, pp. 213–231, 2009.
- C. T. Anh and P. Q. Hung, “Global existence and long-time behavior of solutions to a class of degenerate parabolic equations,” Annales Polonici Mathematici, vol. 93, no. 3, pp. 217–230, 2008.
- C. T. Anh, N. M. Chuong, and T. D. Ke, “Global attractor for the m-semiflow generated by a quasilinear degenerate parabolic equation,” Journal of Mathematical Analysis and Applications, vol. 363, no. 2, pp. 444–453, 2010.
- C. T. Anh and T. D. Ke, “Long-time behavior for quasilinear parabolic equations involving weighted p-Laplacian operators,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 71, no. 10, pp. 4415–4422, 2009.
- C. T. Anh, N. D. Binh, and L. T. Thuy, “On the global attractors for a class of semilinear degenerate parabolic equations,” Annales Polonici Mathematici, vol. 98, no. 1, pp. 71–89, 2010.
- C. T. Anh and L. T. Thuy, “Notes on global attractors for a class of semilinear degenerate parabolic equations,” Journal of Nonlinear Evolution Equations and Applications, vol. 4, pp. 1–16, 2012.
- N. I. Karachalios and N. B. Zographopoulos, “On the dynamics of a degenerate parabolic equation: global bifurcation of stationary states and convergence,” Calculus of Variations and Partial Differential Equations, vol. 25, no. 3, pp. 361–393, 2006.