A nonlocal phase-field model with nonconstant specific heat

Interfaces and Free Boundaries

Volumn 9, Issue 2, 2007, Pages 285-306

  Krejčí, Pavel ^a,b   Rocca, Elisabetta ^c   Sprekels, Jürgen ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b MATHEMATICAL INSTITUTE   (Czech Republic)

^c UNIVERSITY OF MILAN   (Italy)

Author keywords

Integrodifferential equations; Nonlocal models; Phase transitions

Indexed keywords

EID: 34547323506     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/165     Document Type: Article

References (28)

1. p-bounds of solutions of reaction-diffusion equations. Comm. Partial Differential Equations 4 (1979), 827-868. Zbl 0421.35009 MR 0537465
2. BATES, P., & CHMAJ, A. An integrodifferential model for phase transitions: stationary solutions in higher space dimensions. J. Statist. Phys. 95 (1999), 1119-1139. Zbl 0958.82015 MR 1712445
3. BATES, P., & HAN, J. The Neumann boundary problem for a nonlocal Cahn-Hilliard equation. J. Differential Equations 212 (2005), 235-277. Zbl 1081.45004 MR 2129092
4. BERS, L., JOHN, F., & SCHECHTER, M. Partial Differential Equations. Wiley (1964). Zbl 0126.00207 MR 0163043
5. BREZIS, H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hubert. North-Holland Math. Stud. 5, North-Holland, Amsterdam (1973). Zbl 0252.47055 MR 0348562
6. BROKATE, M., & SPREKELS, J. Hysteresis and Phase Transitions. Appl. Math. Sci. 121, Springer, New York (1996). Zbl 0951.74002 MR 1411908
7. CAGINALP, G. An analysis of a phase field model of a free boundary. Arch. Ration. Mech. Anal. 92 (1986), 205-245. Zbl 0608.35080 MR 0816623
8. CAHN, J., & HILLIARD, J. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28 (1958), 258-267.
9. CHEN, C. K., & FIFE, P. C. Nonlocal models of phase transitions in solids. Adv. Math. Sci. Appl. 10 (2000), 821-849. Zbl 0977.74044 MR 1807453
10. COLLI, P., KREJČÍ, P., ROCCA, E., & SPREKELS, J. Nonlinear evolution inclusions arising from phase change models. Czechoslovak Math. J., to appear.
11. FEIREISL, E., ISSARD-ROCH, F., & PETZELTOVÁ, H. A non-smooth version of the Łojasiewicz- Simon theorem with applications to nonlocal phase-field systems. J. Differential Equations 199 (2004), 1-21. Zbl 1062.35152 MR 2041509
12. GAJEWSKI, H. On a nonlocal model of non-isothermal phase separation. Adv. Math. Sci. Appl. 12 (2002), 569-586. Zbl 1039.80001 MR 1943981
13. GAJEWSKI, H., & GRIEPENTROG, J. A. A descent method for the free energy of multicomponent systems. Discrete Contin. Dyn. Syst. 15 (2006), 505-528. MR 2199441
14. GAJEWSKI, H., & ZACHARIAS, K. On a nonlocal phase separation model. J. Math. Anal. Appl. 286 (2003), 11-31. Zbl 1032.35078 MR 2009615
15. GIACOMIN, G., & LEBOWITZ, J. L. Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits. J. Statist. Phys. 87 (1997), 37-61. Zbl 0937.82037 MR 1453735
16. GIACOMIN, G., & LEBOWITZ, J. L. Phase segregation dynamics in particle systems with long range interactions. II. Interface motion. SIAM J. Appl. Math. 58 (1998), 1707-1729. Zbl 1015.82027 MR 1638739
17. GRASSELLI, M., PETZELTOVÁ, H., & SCHIMPERNA, G. A nonlocal phase-field system with inertial term. Quart. Appl. Math., to appear.
18. GRIEPENTROG, J. A. On the unique solvability of a nonlocal phase separation problem for multicomponent systems. Nonlocal Elliptic and Parabolic Problems, Banach Center Publ. 66, Inst. Math., Polish. Acad. Sci. (2004), 153-164. Zbl pre02122832 MR 2143362
19. KREJČÍ , P., ROCCA, E., & SPREKELS, J, Nonlocal temperature-dependent phase-field models for non-isothermal phase transitions. J. London Math. Soc., to appear.
20. KREJČÍ, P., & SPREKELS, J. Nonlocal phase-field models for non-isothermal phase transitions and hysteresis. Adv. Math. Sci. Appl. 14 (2004), 593-612. Zbl 1073.74042 MR 2111831
21. KREJČÍ, P., & SPREKELS, J. Long time behaviour of a singular phase transitions model. Discrete Contin. Dyn. Syst. A 15 (2006), 1119-1135. MR 2224500
22. KREJČÍ, P., SPREKELS, J., & ZHENG, S. Asymptotic behaviour for a phase-field system with hysteresis. J. Differential Equations 175 (2001), 88-107. Zbl 1021.35131 MR 1849225
23. KREJČÍ, P., & ZHENG, S. Pointwise asymptotic convergence of solutions for a phase separation model. Discrete Contin. Dyn. Syst. 16 (2006), 1-18. Zbl 1105.80008 MR 2221733
24. LIONS, J.-L., & MAGENES, E. Problèmes aux limites non homogènes et applications. Vol. 1, Dunod, Paris (1968). Zbl 0165.10801 MR 0247244
25. PENROSE, O., & FIFE, P. C. Thermodynamically consistent models of phase field type for the kinetics of phase transitions. Phys. D 43 (1990), 44-62. Zbl 0709.76001 MR 1060043
26. SPREKELS, J., & ZHENG, S. Global existence and asymptotic behaviour for a nonlocal phase-field model for non-isothermal phase transitions. J. Math. Anal. Appl. 279 (2003), 97-110. Zbl 1023.35051 MR 1970493
27. VISINTIN, A. Models of Phase Transitions. Birkhäuser, Boston (1996). Zbl 0882.35004 MR 1423808
28. VAN DER WAALS, J. D. The thermodynamic theory of capillarity flow under the hypothesis of a continuous variation in density. Verhandelingen der Koninklijke Nederlandsche Akademie van Wetenshappen te Amsterdam 1 (1893), 1-56.