Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Long-time behaviour of a thermomechanical model for adhesive contact
Pages: 273 - 309, Volume 4, Issue 2, April 2011

doi:10.3934/dcdss.2011.4.273      Abstract        References        Full text (674.9K)           Related Articles

Elena Bonetti - Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy (email)
Giovanna Bonfanti - Dipartimento di Matematica Università di Brescia, Via Valotti 9, I–25133 Brescia, Italy (email)
Riccarda Rossi - Dipartimento di Matematica, Università di Brescia, Via Valotti 9, I–25133 Brescia, Italy (email)

1 V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Spaces," Noordhoff, Leyden, 1976.       
2 E. Bonetti, G. Bonfanti and R. Rossi, Global existence for a contact problem with adhesion, Math. Meth. Appl. Sci., 31 (2008), 1029-1064.       
3 E. Bonetti, G. Bonfanti and R. Rossi, Well-posedness and long-time behaviour for a model of contact with adhesion, Indiana Univ. Math. J., 56 (2007), 2787-2819.       
4 E. Bonetti, G. Bonfanti and R. Rossi, Thermal effects in adhesive contact: Modelling and analysis, Nonlinearity, 22 (2009), 2697-2731.       
5 E. Bonetti, P. Colli, M. Fabrizio and G. Gilardi, Global solution to a singular integrodifferential system related to the entropy balance, Nonlinear Anal., 66 (2007), 1949-1979.       
6 E. Bonetti, P. Colli, M. Fabrizio and G. Gilardi, Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 1001-1026.       
7 E. Bonetti, P. Colli and M. Frémond, A phase field model with thermal memory governed by the entropy balance, Math. Models Methods Appl. Sci., 13 (2003), 1565-1588.       
8 E. Bonetti, M. Frémond and E. Rocca, A new dual approach for a class of phase transitions with memory: Existence and long-time behaviour of solutions, J. Math. Pures Appl., 88 (2007), 455-481.       
9 H. Brézis, "Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert," North-Holland, Amsterdam, 1973.       
10 P. Colli, On some doubly nonlinear evolution equations in Banach spaces, Japan J. Indust. Appl. Math., 9 (1992), 181-203.       
11 P. Colli, G. Gilardi, P. Laurençot and A. Novick-Cohen, Existence and long-time behavior of the conserved phase-field system with memory, Discrete Contin. Dynamic Systems, 5 (1999), 375-390.       
12 E. Feireisl and G. Schimperna, Large time behaviour of solutions to Penrose-Fife phase change models, Math. Methods Appl. Sci., 28 (2005), 2117-2132.       
13 M. Frémond, "Non-smooth Thermomechanics," Springer-Verlag, Berlin, 2002.       
14 M. Grasselli, H. Petzeltová and G. Schimperna, Long-time behavior of solutions to the Caginalp system with singular potential, Z. Anal. Anwend., 25 (2006), 51-72.       
15 A. Haraux, "Systèmes Dynamiques Dissipatifs et Applications," Masson, Paris, 1991.       
16 P. Krejčí and S. Zheng, Pointwise asymptotic convergence of solutions for a phase separation model, Discrete Contin. Dyn. Syst., 16 (2006), 1-18.       
17 P. Rybka and K-H. Hoffmann, Convergence of solutions to Cahn-Hilliard equation, Comm. Partial Differential equations, 24 (1999), 1055-1077.       
18 J. Simon, Compact sets in the space $L^p(0,T; B)$, Ann. Mat. Pura Appl. (4), 146 (1987), 65-96.       

Go to top