Hysteresis in phase-field models with thermal memory

Mathematical Methods in the Applied Sciences

Volumn 23, Issue 10, 2000, Pages 909-922

  Gilardi, Gianni ^a   Krejč, Pavel ^b,c   Sprekels, Jürgen ^c  

^a UNIVERSITY OF PAVIA   (Italy)

^b MATHEMATICAL INSTITUTE   (Czech Republic)

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

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONVOLUTION; HEAT FLUX; HYSTERESIS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PHASE TRANSITIONS; TEMPERATURE; THEOREM PROVING;

PHASE FIELD MODELS; THERMAL MEMORY;

INITIAL VALUE PROBLEMS;

EID: 0034223902     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/1099-1476(20000710)23:10<909::AID-MMA142>3.0.CO;2-E     Document Type: Article

References (21)

1. Baiocchi C. Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert. Ann. Mat. Pura Appl. (4) 1967; 76: 233-304.
2. Bonfanti G, Colli P, Grasselli M, Luterotti F. Nonsmooth kernels in a phase relaxation problem with memory. Nonlinear Anal. 1998; 32: 455-465
3. Brokate M, Sprekels J. Hysteresis and Phase Transitions, Appl. Math. Sci., Vol. 121. Springer: New York, 1996.
4. Colli P, Grasselli M. Phase transitions in materials with memory. In Progress in Partial Differential Equations: Calculus of Variations, Applications, Bandle C, Bemelmans J, Chipot M, Grüter M, Saint Jean Paulin J (eds), Pitman Res. Notes Math. Ser. Vol. 267. Longman Sci. Tech: Harlow, 1992; 173-186.
5. Colli P, Grasselli M. An existence result for a hyperbolic phase transition problem with memory. Appl. Math. Lett. 1992; 5: 99-102.
6. Colli P, Grasselli M. Phase transition problems in materials with memory. J. Integral Equations Appl. 1993; 5: 1-22.
7. Colli P, Grasselli M. Phase change problems in materials with memory. In Proceedings of the seventh European Conference on Mathematics in Industry, Fasano A, Primicerio M (eds). Teubner: Stuttgart, 1994; 183-190.
8. Colli P, Sprekels J. Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory. J. Differential Equations 1998; 142: 54-77.
9. Frémond M, Visintin A. Dissipation dans le changement de phase. Surfusion. Changement de phase irreversible. C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 1985; 301: 1265-1268.
10. Gentili G, Giorgi C. Thermodynamic properties and stability for the heat flux equation with linear memory. Quart. Appl. Math. 1993; 51: 343-362.
11. Joseph DD, Preziosi L. Heat waves. Rev. Mod Phys. 1989; 61: 41-73.
12. Joseph DD, Preziosi L. Addendum to the paper "Heat waves". [Rev. Mod. Phys. 1989; 61: 41-73], Rev. Mod. Phys. 1990; 62: 375-391.
13. Joseph DD, Preziosi L. Addendum to the paper "Heat waves". [Rev. Mod. Phys. 1989; 61: 41-73], Rev. Mod. Phys. 1990; 62: 375-391.
14. Krasnosel'skii MA, Pokrovskii AV. Systems with Hysteresis. Springer: Heidelberg, 1989 (Russian edition: Nauka: Moscow, 1983).
15. Krejčí P. Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Gakuto Int. Series Math. Sci & Appl., Vol. 8. Gakkōtosho: Tokyo, 1996.
16. Krejčí P, Sprekels J. A hysteresis approach to phase-field models. Preprint WIAS No. 364, 1997, Nonlinear Anal. Ser. A: Theory Methods 2000; 39: 569-586.
17. Krejčí P, Sprekels J. Hysteresis operators in phase-field models of Penrose-Fife type. Appl. Math. 1998; 43: 207-222.
18. Krejčí P, Sprekels J. Phase-field models with hysteresis. Preprint WIAS No. 458, 1998, submitted.
19. Ladyženskaja OA, Solonnikov VA, Ural'ceva NN. Linear and quasilinear equations of parabolic type, Trans. Amer. Math. Soc., Vol. 23. Amer. Math. Soc., Providence, RI, 1968.
20. Visintin A. Differential Models of Hysteresis. Springer: New York, 1994.
21. Visintin A. Models of Phase Transitions, Progress in Nonlinear Differential Equations and Their Applications, Vol. 28. Birkhäuser: Basel, 1996.