Asymptotic behavior of solutions of a conserved phase-field system with memory

Journal of Integral Equations and Applications

Volumn 15, Issue 3, 2003, Pages 217-240

  Aizicovici, Sergiu ^a   Petzeltová, Hana ^b  

^a OHIO UNIVERSITY   (United States)

^b MATHEMATICAL INSTITUTE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645139538     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181074968     Document Type: Article

References (26)

1. S. Aizicovici and V. Barbu, Existence and asymptotic results for a system of integro-partial differential equations, Nonlinear Differential Equations Appl. 3 (1996), 1 18.
2. S. Aizicovici and E. Feireisl, Long-time stabilization of solutions to a phasefield model with memory, J. Evol. Equations 1 (2001), 69 84.
3. S. Aizicovici, E. Feireislan d F. Issard-Roch, Long-time convergence of solutions to the phase-field system, Math. Methods Appl. Sci. 24 (2000), 277 287.
4. B. Aulbach, Continuous and discrete dynamics near manifolds of equilibria, Lecture Notes in Math., vol. 1058, Springer-Verlag, New York, 1984.
5. D. Brochet, D. Hilhorst and X. Chen, Finite dimensional exponential attractor for the phase field model, Appl. Anal. 49 (1993), 197 212.
6. D. Brochet, D. Hilhorst and A. Novick-Cohen, Maximal attractor and inertial sets for a conserved phase field model, Adv. Differential Equations 1 (1996), 547 578.
7. G. Caginalp, The dynamics of a conserved phase field system: Stefan-like, Hele-Shaw, and Cahn-Hilliard models as asymptotic limits, IMA J. Appl. Math. 44 (1990), 77 94.
8. B.D. Coleman and M.E. Gurtin, Equipresence and constitutive equations for rigid heat conductors, Z. Angew. Math. Phys. 18 (1967), 199 208.
9. P. Colli, G. Gilardi, Ph. Laurençot and A. Novick-Cohen, Uniqueness and longtime behavior for the conserved phase-field model with memory, Discrete Contin. Dynam. Systems 5 (1999), 375 390.
10. C.M. Dafermos, Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. 37 (1970), 297 308.
11. E. Feireisl, F. Issard-Roch and H. Petzeltová, Long-time behaviour and convergence towards equilibria for a conserved phase field model, Discrete Contin. Dynam. Systems 11 (2004), 239 252.
12. E. Feireisla nd F. Simondon, Convergence for semilinear degenerate parabolic equations in several space dimensions, J. Dynam. DifferentialEq uations 12 (2000), 647 673.
13. E. Feireislan d P. Takáč, Long-time stabilization of solutions to the Ginzburg- Landau equations of superconductivity, Monatsh. Math. 133 (2001), 197 221.
14. C. Giorgi, M. Grasselli and V. Pata, Uniform attractors for a phase-field model with memory and quadratic nonlinearity, Indiana Univ. Math. J. 48 (1999), 1129 1181.
15. M. Grasselli, V. Pata and F.M. Vegni, Longterm dynamics of a conserved phase-field system with memory, Asymptotic Anal. 33 (2003), 261 320.
16. A. Haraux and M.A. Jendoubi, Convergence of solutions of second-order gradient-like systems with analytic nonlinearities, J. Differential Equations 144 (1998), 313 320.
17. K.-H. Hoffmann and P. Rybka, Convergence of solutions to Cahn-Hilliard equation, Comm. Partial Differential Equations 24 (1999), 1055 1077.
18. M.A. Jendoubi, Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity, J. Differential Equations 144 (1998), 302 312.
19. S. Lojasiewicz, Une propriété topologique des sous ensembles analytiques réels, Col l oq. CNRS, Les équations aux dérivées partielles, 117, 1963.
20. A. Novick-Cohen, Conserved phase-field equations with memory, in Curvature flows and related topics (Levico, 1994), Gakuto Internat. Ser. Math. Sci. Appl., vol. 5, Tokyo, 1995, pp. 179 197.
21. P. Poláčik and K.P. Rybakowski, Nonconvergent bounded trajectories in semilinear heat equations, J. Differential Equations 124 (1996), 472 494.
22. J. Prüss, Evolutionary integral equations and applications, Birkhäuser, Basel, 1993.
23. p(0,T;B), Ann. Mat. Pura Appl. 146 (1987), 65 96.
24. L. Simon, Asymptotics for a class of non-linear evolution equations, with applications to geometric problems, Ann. of Math. 118 (1983), 525 571.
25. F.M. Vegni, Dissipativity of a conserved phase-field model with memory, Discrete Contin. Dynam. Systems 9 (2003), 949 968.
26. E. Zeidler, Nonlinear functional analysis and its applications, I-IV, Springer-Verlag, New York, 1988.