Well-posedness results for a model of damage in thermoviscoelastic materials
Elena Bonetti; Giovanna Bonfanti
Annales de l'I.H.P. Analyse non linéaire (2008)
- Volume: 25, Issue: 6, page 1187-1208
- ISSN: 0294-1449
Access Full Article
topHow to cite
topBonetti, Elena, and Bonfanti, Giovanna. "Well-posedness results for a model of damage in thermoviscoelastic materials." Annales de l'I.H.P. Analyse non linéaire 25.6 (2008): 1187-1208. <http://eudml.org/doc/78828>.
@article{Bonetti2008,
author = {Bonetti, Elena, Bonfanti, Giovanna},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {damage; thermoviscoelasticity; well-posedness results; non-linear evolution inclusions},
language = {eng},
number = {6},
pages = {1187-1208},
publisher = {Elsevier},
title = {Well-posedness results for a model of damage in thermoviscoelastic materials},
url = {http://eudml.org/doc/78828},
volume = {25},
year = {2008},
}
TY - JOUR
AU - Bonetti, Elena
AU - Bonfanti, Giovanna
TI - Well-posedness results for a model of damage in thermoviscoelastic materials
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 6
SP - 1187
EP - 1208
LA - eng
KW - damage; thermoviscoelasticity; well-posedness results; non-linear evolution inclusions
UR - http://eudml.org/doc/78828
ER -
References
top- [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. Zbl0153.17202MR223697
- [2] Barbu V., Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1976. Zbl0328.47035MR390843
- [3] Bonetti E., Bonfanti G., Existence and uniqueness of the solution to a 3D thermoviscoelastic system, Electron. J. Differential Equations50 (2003) 1-15. Zbl1034.74022MR1971116
- [4] Bonetti E., Schimperna G., Local existence to Frémond's model for damaging in elastic materials, Contin. Mech. Thermodyn.16 (2004) 319-335. Zbl1066.74048MR2061321
- [5] Bonetti E., Schimperna G., Segatti A., On a doubly nonlinear model for the evolution of damaging in viscoelastic materials, J. Differential Equations218 (2005) 91-116. Zbl1078.74048MR2174968
- [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. Zbl0956.35122MR1769184
- [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. Zbl1092.80006MR2004090
- [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. Zbl0252.47055MR348562
- [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. Zbl0489.73124MR653464
- [10] Francfort G.A., Suquet P., Homogenization and mechanical dissipation in thermoviscoelasticity, Arch. Ration. Mech. Anal.96 (1986) 265-293. Zbl0621.73044MR855306
- [11] Frémond M., Non-smooth Thermomechanics, Springer-Verlag, Berlin, 2001. Zbl0990.80001MR1885252
- [12] Frémond M., Kenmochi N., Damage problems for viscous locking materials, Adv. Math. Sci. Appl.16 (2006) 697-716. Zbl1158.74310MR2356296
- [13] Frémond M., Kuttler K.L., Nedjar B., Shillor M., One dimensional models of damage, Adv. Math. Sci. Appl.8 (1998) 541-570. Zbl0915.73041MR1657215
- [14] Lions J.L., Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
- [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. Zbl1032.35109MR1900495
- [16] Nirenberg L., On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3)13 (1959) 115-162. Zbl0088.07601MR109940
- [17] Sassetti M., Tarsia A., Su un'equazione non lineare della corda vibrante, Ann. Mat. Pura Appl.161 (1992) 1-42. Zbl0780.35016MR1174809
- [18] Schimperna G., Stefanelli U., Positivity of the temperature for phase transitions with micro-movements, Nonlinear Anal. Real World Appl.8 (2007) 257-266. Zbl1116.80015MR2268083
- [19] Simon J., Compact sets in the space , Ann. Mat. Pura Appl. (4)146 (1987) 65-96. Zbl0629.46031MR916688
Citations in EuDML Documents
top- Elena Bonetti, Michel Frémond, Analytical results on a model for damaging in domains and interfaces
- Elena Bonetti, Michel Frémond, Analytical results on a model for damaging in domains and interfaces
- Elisabetta Rocca, Riccarda Rossi, Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.