Abstract evolution equations for viscoelastic frictional contact problems

  • B. Awbi
  • M. Sofonea
  • M. Rochdi

DOI: 10.1007/s000330050196

Cite this article as:
Awbi, B., Sofonea, M. & Rochdi, M. Z. angew. Math. Phys. (2000) 51: 218. doi:10.1007/s000330050196

Abstract.

We analyze a nonlinear abstract evolution problem describing a class of frictional contact processes between a viscoelastic body and a foundation. The problem is set as a time-dependent differential inclusion. The existence of a unique solution is established using the theory of elliptic variational inequalities and Banach's fixed point theorem. A dual formulation of the problem is also introduced and an equivalence result between the two problems is proved. Finally, the abstract results obtained are used to solve some frictional contact problems for viscoelastic materials.

Key words. Evolution equation, strongly monotone operator, subdifferential, fixed point, dual problem, nonlinear viscoelastic material, bilateral contact, Coulomb's friction law, normal compliance.

Copyright information

© Birkhäuser Verlag, Basel, 2000

Authors and Affiliations

  • B. Awbi
    • 1
  • M. Sofonea
    • 1
  • M. Rochdi
    • 2
  1. 1.Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan, FranceFR
  2. 2.Institut de Recherche en Mathématiques et Informatique Appliquées, Université de La Réunion, 97715 Saint-Denis, Ile de La Réunion, FranceFR