A convergence result for evolutionary variational inequalities and applications to antiplane frictional contact problems

Volume 31 / 2004

Mircea Sofonea, Mohamed Ait Mansour Applicationes Mathematicae 31 (2004), 55-67 MSC: 74M10, 74M15, 49J40. DOI: 10.4064/am31-1-5

Abstract

We consider a class of evolutionary variational inequalities depending on a parameter, the so-called viscosity. We recall existence and uniqueness results, both in the viscous and inviscid case. Then we prove that the solution of the inequality involving viscosity converges to the solution of the corresponding inviscid problem as the viscosity converges to zero. Finally, we apply these abstract results in the study of two antiplane quasistatic frictional contact problems with viscoelastic and elastic materials, respectively. For each of the problems we prove the existence of a unique weak solution; we also provide convergence results, together with their mechanical interpretation.

Authors

  • Mircea SofoneaLaboratoire de Théorie des Systèmes
    Université de Perpignan
    52 Avenue de Villeneuve
    66860 Perpignan, France
    e-mail
  • Mohamed Ait MansourLaboratoire d'Arithmétique,
    de Calcul formel et d'Optimisation
    Université de Limoges
    123 Avenue A. Thomas
    87060 Limoges, France
    e-mail

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