In this paper we study a dynamic unilateral contact problem with friction for a cracked viscoelastic body. The viscoelastic model is characterized by Kelvin–Voigt's law and a nonlocal friction law is investigated here. The existence of a solution to the problem is obtained by using a penalty method. Several estimates are obtained on the solution to the penalized problem, which enable us to pass to the limit by using compactness results.
Dans ce travail, on s'intéresse à un problème dynamique de contact unilatéral avec frottement non local pour un milieu viscoélastique fissuré, suivant une loi de comportement de Kelvin–Voigt. L'existence d'une solution du problème est obtenue par une méthode de pénalisation. Le passage à la limite est justifié par plusieurs estimations et par quelques résultats de compacité.
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Marius Cocou 1; Gilles Scarella 2
@article{CRMATH_2004__338_4_341_0, author = {Marius Cocou and Gilles Scarella}, title = {Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body}, journal = {Comptes Rendus. Math\'ematique}, pages = {341--346}, publisher = {Elsevier}, volume = {338}, number = {4}, year = {2004}, doi = {10.1016/j.crma.2003.12.013}, language = {en}, }
TY - JOUR AU - Marius Cocou AU - Gilles Scarella TI - Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body JO - Comptes Rendus. Mathématique PY - 2004 SP - 341 EP - 346 VL - 338 IS - 4 PB - Elsevier DO - 10.1016/j.crma.2003.12.013 LA - en ID - CRMATH_2004__338_4_341_0 ER -
Marius Cocou; Gilles Scarella. Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body. Comptes Rendus. Mathématique, Volume 338 (2004) no. 4, pp. 341-346. doi : 10.1016/j.crma.2003.12.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.12.013/
[1] Existence, uniqueness, and regularity results for the two-body contact problem, Appl. Math. Optim., Volume 15 (1987), pp. 251-277
[2] Analysis of a class of implicit evolution inequalities associated to viscoelastic dynamic contact problems with friction, Int. J. Engrg. Sci., Volume 38 (2000), pp. 1535-1552
[3] Existence of solutions of a dynamic Signorini's problem with nonlocal friction in viscoelasticity, Z. Angew. Math. Phys. (ZAMP), Volume 53 (2002), pp. 1099-1109
[4] Dynamic contact problems with given friction for viscoelastic bodies, Czechoslovak Math. J., Volume 46 (1996) no. 121, pp. 475-487
[5] A boundary thin obstacle problem for a wave equation, Comm. Partial Differential Equations, Volume 14 (1989), pp. 1011-1026
[6] Dynamic bilateral contact with discontinuous friction coefficient, Nonlinear Anal., Volume 45 (2001), pp. 309-327
[7] A wave problem in a half-space with a unilateral constraint at the boundary, J. Differential Equations, Volume 53 (1984), pp. 309-361
[8] Multidimensional contact problems in thermoelasticity, SIAM J. Appl. Math., Volume 58 (1998), pp. 1307-1337
[9] Surface perturbation of an elastodynamic contact problem with friction, European J. Appl. Math., Volume 14 (2003), pp. 465-483
[10] One-dimensional viscoelastodynamics with Signorini boundary conditions, C. R. Acad. Sci. Paris, Ser. I, Volume 334 (2002), pp. 983-988
[11] Analysis of a time discretisation for an implicit variational inequality modelling dynamic contact problems with friction, Math. Methods Appl. Sci., Volume 24 (2001), pp. 491-511
[12] Compact sets in the space Lp(0,T;B), Ann. Mat. Pura Appl., Volume 146 (1987), pp. 65-96
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