Convergence results for a phase transition model with vanishing microscopic acceleration

Mathematical Models and Methods in Applied Sciences

Volumn 14, Issue 3, 2004, Pages 375-392

  Bonfanti, Giovanna ^a   Luterotti, Fabio ^a  

^a UNIVERSITY OF BRESCIA   (Italy)

Author keywords

Existence and uniqueness results; Microscopic accelerations; Phase changes

Indexed keywords

EID: 7244245353     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202504003271     Document Type: Article

References (16)

1. C. Baiocchi, Sulle equazioni differenziali astratte lineari del primo e del seconde ordine negli spazi di Hilbert, Ann. Mat. Pura Appl. 76 (1967) 233-304.
2. G. Bonfanti, M. Frémond and F. Luterotti, Global solution to a nonlinear system for irreversible phase changes, Adv. Math. Sci. Appl. 10 (2000) 1-24.
3. G. Bonfanti, M. Frémond and F. Luterotti, Local solutions to the full model of phase transitions with dissipation, Adv. Math. Sci. Appl. 11 (2001) 791-810.
4. G. Bonfanti, M. Frémond and F. Luterotti, Existence and uniqueness results to a phase transition model based on microscopic accelerations and movements, Nonlinear Anal. Real World Appl. 1 (2004) 123-140.
5. G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal. 92 (1986) 205-245.
6. P. Colli, G. Gilardi and M. Grasselli, Well-posedness of the weak formulation for the phase-field model with memory, Adv. Differential Equations 2 (1997) 487-508.
7. P. Colli, F. Luterotti, G. Schimperna and U. Stefanelli, Global existence for a, class of generalized systems for irreversible phase changes, NoDEA Nonlinear Differential Equations Appl. 9 (2002) 255-276.
8. M. Frémond, Non-smooth Thermomechanics (Springer-Verlag, 2001).
9. J. Jarusek, J. Málek, J. Necas and V. Sverák, Variational inequality for a viscous drum vibrating in the presence of an obstacle, Bend. Mat. Ser. VII 12 (1992) 943-958.
10. J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Nonlinéaires (Dunod-Gauthier Villars, 1969).
11. F. Luterotti, A unilateral problem for a nonlinear hyperbolic operator, Rend. Mat. Ser. VII 17 (1997) 21-36.
12. F. Luterotti, G. Schimperna, and U. Stefanelli, Existence result for a nonlinear model related to irreversible phase changes, Math. Mod. Meth. Appl. Sci. 11 (2001) 809-825.
13. F. Luterotti, G. Schimperna and U. Stefanelli, Existence result for a nonlinear model related to irreversible phase changes, Quart. Appl. Math. 60 (2002) 301-316.
14. M. Sassetti and A. Tarsia, Su un'equazione non lineare della corda vibrante, Ann. Mat. Pura Appl. 161 (1992) 1-42.
15. P(0, T; B), Ann. Mat. Pura Appl. 146 (1987) 65-96.
16. C. F. Vasconcellos and L. M. Teixeira, Strong solutions and exponential decay for a non-linear hyperbolic equation, Appl. Anal. 51 (1993) 155-173.