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

Mircea Sofonea¹ ; Mohamed Ait Mansour²

¹ Laboratoire de Théorie des Systèmes Université de Perpignan 52 Avenue de Villeneuve 66860 Perpignan, France
² Laboratoire d'Arithmétique, de Calcul formel et d'Optimisation Université de Limoges 123 Avenue A. Thomas 87060 Limoges, France

Applicationes Mathematicae, Tome 31 (2004) no. 1, pp. 55-67.

Résumé

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.

Détail

DOI : 10.4064/am31-1-5

Keywords: consider class evolutionary variational inequalities depending parameter so called viscosity recall existence uniqueness results viscous inviscid prove solution inequality involving viscosity converges solution corresponding inviscid problem viscosity converges zero finally apply these abstract results study antiplane quasistatic frictional contact problems viscoelastic elastic materials respectively each problems prove existence unique weak solution provide convergence results together their mechanical interpretation