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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...

We provide a sensitivity result for the solutions to the following finite-dimensional quasi-variational inequality $$QVIu\in K\left(u\right),〈C\left(u\right),v-u〉\ge 0,\mathrm{\forall }v\in K\left(u\right),$$ when both the operator $C$ and the convex $K$ are perturbed. In particular, we prove the Hölder continuity of the solution sets of the problems perturbed around the original problem. All the results may be extended to infinite-dimensional (QVI).