Well-posedness results for a model of damage in thermoviscoelastic materials
Bonetti, Elena ; Bonfanti, Giovanna
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008), p. 1187-1208 / Harvested from Numdam
@article{AIHPC_2008__25_6_1187_0,
     author = {Bonetti, Elena and Bonfanti, Giovanna},
     title = {Well-posedness results for a model of damage in thermoviscoelastic materials},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {25},
     year = {2008},
     pages = {1187-1208},
     doi = {10.1016/j.anihpc.2007.05.009},
     mrnumber = {2466326},
     zbl = {1152.35505},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_6_1187_0}
}
Bonetti, Elena; Bonfanti, Giovanna. Well-posedness results for a model of damage in thermoviscoelastic materials. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) pp. 1187-1208. doi : 10.1016/j.anihpc.2007.05.009. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_6_1187_0/

[1] Baiocchi C., Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert, Ann. Mat. Pura Appl. (IV) 76 (1967) 233-304. | MR 223697 | Zbl 0153.17202

[2] Barbu V., Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1976. | MR 390843 | Zbl 0328.47035

[3] Bonetti E., Bonfanti G., Existence and uniqueness of the solution to a 3D thermoviscoelastic system, Electron. J. Differential Equations 50 (2003) 1-15. | MR 1971116 | Zbl 1034.74022

[4] Bonetti E., Schimperna G., Local existence to Frémond's model for damaging in elastic materials, Contin. Mech. Thermodyn. 16 (2004) 319-335. | MR 2061321 | Zbl 1066.74048

[5] Bonetti E., Schimperna G., Segatti A., On a doubly nonlinear model for the evolution of damaging in viscoelastic materials, J. Differential Equations 218 (2005) 91-116. | MR 2174968 | Zbl 1078.74048

[6] Bonfanti G., Frémond M., Luterotti F., Global solution to a nonlinear system for irreversible phase changes, Adv. Math. Sci. Appl. 10 (2000) 1-24. | MR 1769184 | Zbl 0956.35122

[7] Bonfanti G., Frémond M., Luterotti F., Existence and uniqueness results to a phase transition model based on microscopic accelerations and movements, Nonlinear Anal. Real World Appl. 5 (2004) 123-140. | MR 2004090 | Zbl 1092.80006

[8] Brézis H., Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Math. Studies, vol. 5, North-Holland, Amsterdam, 1973. | MR 348562 | Zbl 0252.47055

[9] Dafermos C.M., Global smooth solutions to the initial boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity, SIAM J. Math. Anal. 13 (1982) 397-408. | MR 653464 | Zbl 0489.73124

[10] Francfort G.A., Suquet P., Homogenization and mechanical dissipation in thermoviscoelasticity, Arch. Ration. Mech. Anal. 96 (1986) 265-293. | MR 855306 | Zbl 0621.73044

[11] Frémond M., Non-smooth Thermomechanics, Springer-Verlag, Berlin, 2001. | MR 1885252 | Zbl 0990.80001

[12] Frémond M., Kenmochi N., Damage problems for viscous locking materials, Adv. Math. Sci. Appl. 16 (2006) 697-716. | MR 2356296 | Zbl 1158.74310

[13] Frémond M., Kuttler K.L., Nedjar B., Shillor M., One dimensional models of damage, Adv. Math. Sci. Appl. 8 (1998) 541-570. | MR 1657215 | Zbl 0915.73041

[14] Lions J.L., Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier-Villars, Paris, 1969. | MR 259693 | Zbl 0189.40603

[15] Luterotti F., Schimperna G., Stefanelli U., Global solution to a phase field model with irreversible and constrained phase evolution, Quart. Appl. Math. 60 (2002) 301-316. | MR 1900495 | Zbl 1032.35109

[16] Nirenberg L., On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3) 13 (1959) 115-162. | Numdam | MR 109940 | Zbl 0088.07601

[17] Sassetti M., Tarsia A., Su un'equazione non lineare della corda vibrante, Ann. Mat. Pura Appl. 161 (1992) 1-42. | MR 1174809 | Zbl 0780.35016

[18] Schimperna G., Stefanelli U., Positivity of the temperature for phase transitions with micro-movements, Nonlinear Anal. Real World Appl. 8 (2007) 257-266. | MR 2268083 | Zbl 1116.80015

[19] Simon J., Compact sets in the space L p (0,T;B), Ann. Mat. Pura Appl. (4) 146 (1987) 65-96. | MR 916688 | Zbl 0629.46031