A generalized phase relaxation model with hysteresis

Nonlinear Analysis, Theory, Methods and Applications

Volumn 55, Issue 4, 2003, Pages 381-398

  Luterotti, Fabio ^a   Schimperna, Giulio ^b   Stefanelli, Ulisse ^c  

^a UNIVERSITY OF BRESCIA   (Italy)

^b UNIVERSITY OF PAVIA   (Italy)

^c CNR   (Italy)

Author keywords

Hysteresis operator; Maximum principle; Microscopic movements; Phase relaxation

Indexed keywords

HYSTERESIS; KINETIC THEORY; MAXIMUM PRINCIPLE;

PHASE RELAXATION;

PHASE TRANSITIONS;

EID: 0141569818     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(03)00243-8     Document Type: Article

References (19)

1. Bonfanti G., Frémond M., Luterotti F. Global solution to a nonlinear system for irreversible phase changes. Adv. Math. Sci. Appl. 10:2000;1-24.
2. Bonfanti G., Frémond M., Luterotti F. Local solutions to the full model of phase transition with dissipation. Adv. Math. Sci. Appl. 11:2001;791-810.
3. Brezis H. Opérateurs Maximaux Monotones et Sémi-groupes de Contractions dans les Espaces de Hilbert. North-Holland Math. Studies. Vol. 5:1973;North-Holland, Amsterdam.
4. Brokate M., Sprekels J. Hysteresis and phase transitions. Appl. Math. Sci. Vol. 121:1996;Springer, New York.
5. Colli P., Frémond M., Klein O. Global existence of a solution to a phase field model for supercooling. Nonlinear Anal. Real World Appl. 2:2001;523-539.
6. Colli P., Luterotti F., Schimperna G., Stefanelli U. Global existence for a class of generalized systems for irreversible phase changes. Nonlinear Differential Equations Appl. 9:2002;255-276.
7. Frémond M. Non-smooth Thermomechanics. 2002;Springer, Berlin.
8. Frémond M., Visintin A. Dissipation dans le changement de phase. Surfusion. Changement de phase irréversible. C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers. Sci. Terre. 301:1985;1265-1268.
9. Germain P. Mécanique des Milieux Continus. 1973;Masson, Paris.
10. Krejčí P. Hysteresis, Convexity and dissipation in hyperbolic equations. GAKUTO International Series. Vol. 8:1997;Gakkōtosho, Tokio.
11. Krejčí P., Sprekels J. A hysteresis approach to phase-field models. Nonlinear Anal. TMA. 39:2000;569-586.
12. Krejčí P., Sprekels J. Phase-field systems for multi-dimensional Prandtl-Ishlinskii operators with non-polyhedral characteristics. Math. Methods Appl. Sci. 25:2002;309-325.
13. P. Krejčí, J. Sprekels, U. Stefanelli, One-dimensional thermo-visco-plastic processes with hysteresis and phase transitions, Adv. Math. Sci. Appl., to appear.
14. Ladyzhenskaya O.A., Solonnikov V.A., Ural'ceva N.N. Linear and quasilinear equations of parabolic type. Translations of Mathematical Monographs. Vol. 23:1967;American Mathematical Society, Providence, USA.
15. Luterotti F., Schimperna G., Stefanelli U. Existence result for a nonlinear model related to irreversible phase changes. Math. Models Methods Appl. Sci. 11:2001;808-825.
16. Penrose O., Fife P.C. Thermodynamically consistent models of phase field type for the kinetics of phase transitions. Phys. D. 43:1990;44-62.
17. p(0,T;B) Ann. Mat. Pura Appl. (4). 146:1987;65-96.
18. Visintin A. Stefan problem with phase relaxation. IMA J. Appl. Math. 34:1985;225-245.
19. Visintin A. Differential Models of Hysteresis. 1994;Springer, New York.