Optimal control of differential quasivariational inequalities with applications in contact mechanics

History-dependent hemivariational inequalities with applications to Contact Mechanics

In this paper we survey some of our recent results on the existence and uniqueness of solutions to nonconvex and nonsmooth problems which arise in Contact Mechanics. The approach is based on operator subdifferential inclusions and hemivariational inequalities, and focuses on three aspects. First, we report on results on the second order history-dependent subdifferential inclusions and hemivaria...

On Uniqueness in Evolution Quasivariational Inequalities

We consider a rate independent evolution quasivariational inequality in a Hilbert space X with closed convex constraints having nonempty interior. We prove that there exists a unique solution which is Lipschitz dependent on the data, if the dependence of the Minkowski functional on the solution is Lipschitzian with a small constant and if also the gradient of the square of the Minkowski functio...

Reduced Basis Method for Variational Inequalities in Contact Mechanics

We present an efficient model order reduction method [1] for parametrized elliptic variational inequalities of the first kind: find u ∈ K such that: a(u, v − u;μ) ≥ f(v − u;μ), ∀v ∈ K(μ) where K(μ) := {v ∈ H1(Ω)|Bv ≤ g(μ)}. Motivated by numerous engineering applications that involve contact between elastic body and rigid obstacle, e.g. the obstacle problem [2], we develop a primaldual reduced b...

Generalized Strongly Nonlinear Implicit Quasivariational Inequalities

Extended Well-posedness for Quasivariational Inequalities

In this paper, we introduce the concepts of extended well-posedness for quasivariational inequalities and establish some characterizations. We show that the extended well-posedness is equivalent to the existence and uniqueness of solutions under suitable conditions. In addition, the corresponding concepts of extended well-posedness in the generalized sense are introduced and investigated for qu...