A uniqueness criterion for the Signorini problem with Coulomb friction

SIAM Journal on Mathematical Analysis

Volumn 38, Issue 2, 2006, Pages 452-467

  Renard, Yves ^a  

^a CNRS   (France)

Author keywords

Coulomb friction; Unilateral contact; Uniqueness of solution

Indexed keywords

NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING;

COULOMB FRICTIONS; SOLUTION UNIQUENESS; UNILATERAL CONTACT;

FRICTION;

EID: 33947241227     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/050635936     Document Type: Article

References (15)

1. R. A. ADAMS, Sobolev Spaces, Academic Press, New York, London, 1975.
2. L.-E. ANDERSSON, Existence results for quasistatic contact problems with Coulomb friction, Appl. Math. Optim., 42 (2000), pp. 169-202.
3. G. DUVAUT, Problèmes unilatéraux en mécanique des milieux continus, in Actes du Congrès International des Mathématiciens (Nice 1970), Tome 3, Gauthier-Villars, Paris, 1971, pp. 71-77.
4. G. DUVAUT AND J. L. LIONS, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972.
5. C. ECK AND J. JARUŠEK, Existence results for the static contact problem with Coulomb friction, Math. Models Methods Appl. Sci., 8 (1998), pp. 445-468.
6. R. HASSANI, P. HILD, I. IONESCU, AND N.-D. SAKKI, A mixed finite element method and solution multiplicity for Coulomb fractional contact, Comput. Methods Appl. Mech. Engrg., 192 (2003), pp. 4517-4531.
7. P. HILD, An example of nonuniqueness for the continuous static unilateral contact model with Coulomb friction, C. R. Acad. Sci. Paris, 337 (2003), pp. 685-688.
8. P. HILD, Non-unique slipping in the Coulomb friction model in two-dimensional linear elasticity, Quart. J. Mech. Appl. Math., 57 (2004), pp. 225-235.
9. P. HILD AND Y. RENARD, Local uniqueness and continuation of solutions for the discrete Coulomb friction problem in elastostatics, Quart. Appl. Math., 63 (2005), pp. 553-573.
10. P. HILD AND Y. RENARD, An error estimate for the Signorini problem with Coulomb friction approximated by finite elements, submitted.
11. J. JARUŠEK, Contact problems with bounded friction. Coercive case, Czechoslovak Math. J., 33 (1983), pp. 237-261.
12. N. KIKUCHI AND J. T. ODEN, Contact Problems in Elasticity: A Study of Variational Inequalties and Finite Element Methods, SIAM Stud. Appl. Math. 8, SIAM, Philadelphia, 1988.
13. P. LABORDE AND Y. RENARD, Fixed point strategies for elastostatic frictional contact problems, submitted.
14. V. G. MAZ'YA AND T. O. SHAPOSHNIKOVA, Theory of Multipliers in Spaces of Differentiable Functions, Pitman, Boston, 1985.
15. J. NEČAS, J. JARUŠEK, AND J. HASLINGER, On the solution of variational inequality to the Signorini problem with small friction, Boll. Un. Mat. Ital. B(5), 17 (1980), pp. 796-811.