Convergence to steady state and attractors for doubly nonlinear equations

Journal of Mathematical Analysis and Applications

Volumn 339, Issue 1, 2008, Pages 281-294

  Rougirel, Arnaud ^a  

^a UNIVERSITÉ DE POITIERS   (France)

Author keywords

Convergence to a steady state; Doubly nonlinear equations; Elliptic parabolic and degenerate equations; Global and exponential attractors

Indexed keywords

EID: 35348850755     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.06.028     Document Type: Article

References (21)

1. Alt H., and Luckhaus S. Quasilinear elliptic-parabolic differential equations. Math. Z. 183 3 (1983) 311-341
2. Chill R. On the Lojasiewicz-Simon gradient inequality. J. Funct. Anal. 201 2 (2003) 572-601
3. Chill R., and Jendoubi M. Convergence to steady states in asymptotically autonomous semilinear evolution equations. Nonlinear Anal. 53 7-8 (2003) 1017-1039
4. Eden A., Foias C., Nicolaenko B., and Temam R. Exponential Attractors for Dissipative Evolution Equations. Res. Appl. Math. vol. 37 (1994), Masson, Paris
5. Eden A., Michaux B., and Rakotoson J.-M. Doubly nonlinear parabolic type equations as dynamical systems. J. Dynam. Differential Equations 3 1 (1991) 87-131
6. Efendiev M., and Miranville A. New models of Cahn-Hilliard-Gurtin equations. Contin. Mech. Thermodyn. 16 5 (2004) 441-451
7. 3. C. R. Math. Acad. Sci. Paris Sér. I 330 8 (2000) 713-718
8. Feireisl E., and Simondon F. Convergence for semilinear degenerate parabolic equations in several space dimensions. J. Dynam. Differential Equations 12 3 (2000) 647-673
9. Foias C., and Olson E. Finite fractal dimension and Hölder-Lipschitz parametrization. Indiana Univ. Math. J. 45 3 (1996) 603-616
10. Gurtin M. Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a micro-force balance. Phys. D 92 (1996) 178-192
11. Kavian O. Introduction à la théorie des points critiques et applications aux problèmes elliptiques. Math. Appl. vol. 13 (1993), Springer-Verlag
12. Langlais M., and Phillips D. Stabilization of solutions of nonlinear and degenerate evolution equations. Nonlinear Anal. 9 4 (1985) 321-333
13. Málek J., and Prazák D. Large time behavior via the method of l-trajectories. J. Differential Equations 181 2 (2002) 243-279
14. Miranville A. Finite dimensional global attractor for a class of doubly nonlinear parabolic equations. Cent. Eur. J. Math. 4 1 (2006) 163-182
15. Miranville A., and Rougirel A. Local and asymptotic analysis of the flow generated by the Cahn-Hilliard-Gurtin equation. Z. Angew. Math. Phys. 57 2 (2006) 244-268
16. Miranville A., and Schimperna G. Global solution to a phase transition model based on a microforce balance. J. Evol. Equ. 5 2 (2005) 253-276
17. A. Miranville, S. Zelik, Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type, preprint
18. 1-contraction and uniqueness for quasilinear elliptic-parabolic equations. J. Differential Equations 131 1 (1996) 20-38
19. Robinson J. Infinite-Dimensional Dynamical Systems. An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. Cambridge Texts Appl. Math. (2001), Cambridge Univ. Press
20. Sacks P. Continuity of solutions of a singular parabolic equation. Nonlinear Anal. 7 4 (1983) 387-409
21. Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Appl. Math. Sci. second ed. vol. 68 (1997), Springer-Verlag, New York