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Solvability of a class of thermal dynamical contact problems with subdifferential conditions
1. | Institut d'Ingénierie Informatique de Limoges and LACO, URA-1586, 123 Avenue A. Thomas, 87060 Limoges Cedex |
2. | Université de La Réunion, Département Maths-Info, BP 7151, 15 Avenue René Cassin, 97715 Saint Denis Messag, cedex 09, La Réunion |
References:
[1] |
B. Awbi and O. Chau, Quasistatic Thermovisoelastic Frictional Contact Problem with Damped Response, Applicable Analysis, 83 (2004), 635-648.
doi: 10.1080/00036810410001657233. |
[2] |
V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Spaces," Editura Academiei, Bucharest-Noordhoff, Leyden, 1976. |
[3] |
H. Brézis, Problèmes unilatéraux, J. Math. Pures et Appli., 51 (1972), 1-168. |
[4] |
O. Chau and M. Rochdi, On a dynamic bilateral contact problem with friction for viscoelastic materials, Int. J. of Appli. Math. and Mech., 2 (2006), 41-52. |
[5] |
P. G. Ciarlet, "Mathematical Elasticity, Vol. I, Three-Dimensional Elasticity," North-Holland, 1988. |
[6] |
M. Cocou and G. Scarella, Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body, C.R. Acad. Sci. Paris, Ser. I, 338 (2004), 341-346. |
[7] |
G. Duvaut and J. L. Lions, "Les Inéquations en Mécanique et en Physique," Dunod, Paris, 1972. |
[8] |
Ch. Eck, J. Jarusek and M. Krbec, "Unilateral Contact Problems, Variational Methods and Existence Theorems," Chapman and Hall, 2005.
doi: 10.1201/9781420027365. |
[9] |
D. Goeleven, D. Motreanu, Y. Dumont and M. Rochdi, "Variational and Hemivariational Inequalities, Theory, Methods and Applications, Volume I: Unilateral Analysis and Unilateral Mechanics," Kluwer Academic Publishers, 2003. |
[10] |
J. Jarušek and Ch. Eck, Dynamic contact problems with small Coulomb friction for viscoelastic bodies. Existence of solutions, Mathematical Models and Methods in Applied Sciences, 9 (1999), 11-34.
doi: 10.1142/S0218202599000038. |
[11] |
N. Kikuchi and J. T. Oden, "Contact Problems in Elasticity," SIAM, Philadelphia, 1988.
doi: 10.1137/1.9781611970845. |
[12] |
J. L. Lions, "Quelques méthodes de résolution des problèmes aux limites non linéaires," Dunod et Gauthier-Villars, 1969. |
[13] |
J. Necas, J. Jarusek and J. Haslinger, On the solution of variational inequality to the Signorini problem with small friction, Bolletino U.M.I., 17 (1980), 796-811. |
[14] |
J. Nečas and I. Hlaváček, "Mathematical Theory of Elastic and Elastoplastic Bodies: An introduction," Elsevier, Amsterdam, 1981. |
[15] |
P. D. Panagiotopoulos, "Inequality Problems in Mechanics and Applications," Birkhäuser, Basel, 1985.
doi: 10.1007/978-1-4612-5152-1. |
[16] |
P. D. Panagiotopoulos, "Hemivariational Inequalities, Applications in Mechanics and Engineering," Springer-Verlag, 1993. |
[17] |
Eberhard Zeidler, "Nonlinear Functional Analysis and its Applications, II/A, Linear Monotone Operators," Springer Verlag, 1997. |
show all references
References:
[1] |
B. Awbi and O. Chau, Quasistatic Thermovisoelastic Frictional Contact Problem with Damped Response, Applicable Analysis, 83 (2004), 635-648.
doi: 10.1080/00036810410001657233. |
[2] |
V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Spaces," Editura Academiei, Bucharest-Noordhoff, Leyden, 1976. |
[3] |
H. Brézis, Problèmes unilatéraux, J. Math. Pures et Appli., 51 (1972), 1-168. |
[4] |
O. Chau and M. Rochdi, On a dynamic bilateral contact problem with friction for viscoelastic materials, Int. J. of Appli. Math. and Mech., 2 (2006), 41-52. |
[5] |
P. G. Ciarlet, "Mathematical Elasticity, Vol. I, Three-Dimensional Elasticity," North-Holland, 1988. |
[6] |
M. Cocou and G. Scarella, Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body, C.R. Acad. Sci. Paris, Ser. I, 338 (2004), 341-346. |
[7] |
G. Duvaut and J. L. Lions, "Les Inéquations en Mécanique et en Physique," Dunod, Paris, 1972. |
[8] |
Ch. Eck, J. Jarusek and M. Krbec, "Unilateral Contact Problems, Variational Methods and Existence Theorems," Chapman and Hall, 2005.
doi: 10.1201/9781420027365. |
[9] |
D. Goeleven, D. Motreanu, Y. Dumont and M. Rochdi, "Variational and Hemivariational Inequalities, Theory, Methods and Applications, Volume I: Unilateral Analysis and Unilateral Mechanics," Kluwer Academic Publishers, 2003. |
[10] |
J. Jarušek and Ch. Eck, Dynamic contact problems with small Coulomb friction for viscoelastic bodies. Existence of solutions, Mathematical Models and Methods in Applied Sciences, 9 (1999), 11-34.
doi: 10.1142/S0218202599000038. |
[11] |
N. Kikuchi and J. T. Oden, "Contact Problems in Elasticity," SIAM, Philadelphia, 1988.
doi: 10.1137/1.9781611970845. |
[12] |
J. L. Lions, "Quelques méthodes de résolution des problèmes aux limites non linéaires," Dunod et Gauthier-Villars, 1969. |
[13] |
J. Necas, J. Jarusek and J. Haslinger, On the solution of variational inequality to the Signorini problem with small friction, Bolletino U.M.I., 17 (1980), 796-811. |
[14] |
J. Nečas and I. Hlaváček, "Mathematical Theory of Elastic and Elastoplastic Bodies: An introduction," Elsevier, Amsterdam, 1981. |
[15] |
P. D. Panagiotopoulos, "Inequality Problems in Mechanics and Applications," Birkhäuser, Basel, 1985.
doi: 10.1007/978-1-4612-5152-1. |
[16] |
P. D. Panagiotopoulos, "Hemivariational Inequalities, Applications in Mechanics and Engineering," Springer-Verlag, 1993. |
[17] |
Eberhard Zeidler, "Nonlinear Functional Analysis and its Applications, II/A, Linear Monotone Operators," Springer Verlag, 1997. |
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