Algebraic rate of decay for the excess free energy and stability of fronts for a nonlocal phase kinetics equation with a conservation law. I

Journal of Statistical Physics

Volumn 95, Issue 5-6, 1999, Pages 1069-1117

  Carlen, E A ^a   Carvalho, M C ^a,b   Orlandi, E ^c  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF LISBON   (Portugal)

^c ROMA TRE UNIVERSITY   (Italy)

Author keywords

Fronts; Nonlinear stability; Phase kinetics

Indexed keywords

EID: 0033245873     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004562719554     Document Type: Article

References (22)

1. 1. N. Alikakos, P. W. Bates, and X. Chen, Convergence of the Cahn Hilliard equation to the Hele-Shaw model, Arch. Rat. Mech. Anal. 128:165 205 (1994).
2. 2. A. Asselah, Stability of a wave front for a nonlocal conservative evolution, Proc. Royal Soc. Edinburgh 128A:219-234 (1998).
3. 3. K. Kawasaki, Diffusion constants near the critical point for time-dependent Ising models. I. Phys. Rev. 145:224-230 (1966).
4. 4. J. Bricmont, A. Kupiainen, and J. Taskinen, Stability of Cahn-Hilliard fronts. Comm. Pure & Appl. Math. 52:839-871 (1999).
5. 5. E. A. Carlen, M. C. Carvalho, and E. Orlandi, Free energy inequalities and the rate of relaxation to instanton for interfaces profiles in Glauber dynamics, Nonlinear Differ. Equa. Appl. 5:205-218 (1998).
6. 6. E. A. Carlen, M. C. Carvalho, and E. Orlandi, Algebraic rate of decay for the excess free energy and stability of fronts for a non-local phase kinetics equation with a conservation law II, to appear in Comm. P.D.E.
7. 7. E. A. Carlen, M. C. Carvalho, and E. Orlandi, Existence, uniqueness and regularity properties for a non-local phase kinetics equation with a conservation law, preprint (1998).
8. 8. X. Chen, Global asymptotic limit of solutions of the Cahn Hilliard Equation, J. Diff. Geom. 44(2):262-311 (1996).
9. 9. R. Dal Passo and P. de Mottoni, The heat equation with a nonlocal density dependent advection term, preprint (1991).
10. 10. A. De Masi, T. Gobron, and E. Presutti, Travelling fronts in non local evolution equations. Arch. Rat. Mech. Anal. 132:143 205 (1995).
11. 11. A. De Masi, E. Orlandi, E. Presutti, and L. Triolo, Motion by curvature by scaling non local evolution equations, J. Stat. Phys. 73:543 570 (1993).
12. 12. A. De Masi, E. Orlandi, E. Presutti. and L. Triolo, Glauber evolution with Kac potentials I. Mesoscopic and macroscopic limits, interface dynamics, Nonlinearity 7:633-696 (1994).
13. 13. A. De Masi, E. Orlandi, E. Presutti, and L. Triolo, Stability of the interface in a model of phase separation, Proc. Royal Soc. Edinburgh 124A:1013-1022 (1994).
14. 14. A. De Masi, E. Orlandi, E. Presutti, and L. Triolo, Uniqueness of the inslanton profile and global stability in non local evolution equations, Rendiconte di Matematica. Serie VII, 14 (1994).
15. 15. G. Giacomin and J. Lebowitz, Phase segregation dynamics in particle systems with long range interactions I: Macroscopic limits, J. Stat. Phys. 87:37-61 (1997).
16. 16. G. Giacomin and J. Lebowitz, Phase segregation dynamics in particle systems with long range interactions II: Interface motions, SIAM J. Appl. Math. 58:1707-1729 (1998).
17. 17. R. Glauber, Time-dependent statistics of the Ising model. J. Math. Phys. 4:294-307 (1963).
18. 18. G. Hardy, J. Littlewood, and G. Polya. Inequalities (Cambridge University Press, Cambridge, 1932).
19. 19. M. A. Katsoulakis and P. E. Souganidis, Generalized motion by mean curvature as a macroscopic limit of stochastic Ising models with long range interaction and Glauber dynamics, Comm. Math. Phys. 169:61-97 (1995).
20. 20. J. L. Lebowitz, E. Orlandi, and E. Presutti, A particle model for spinodal decomposition, J. Stat. Phys. 63:933-974 (1991).
21. 21. R. L. Pego, Front migration in the nonlinear Cahn-Hilliard equation, Proc. R. Soc. Lond. A 422:261-278 (1989).
22. 22. H. Weyl, Grüppentheorie and Quantenmechanik, Wissenschaftlich Verlag, Leipzig (1926).