Parabolic Quasi-variational Inequalities with Gradient-Type Constraints

Algorithmic Approach for the Asymptotic Behavior of a System of Parabolic Quasi-Variational Inequalities

In this paper we evaluate the variation in L 1-norm between u i h (T; x) ; i = 1; :::; J the discrete solution calculated at the moment T and u i 1 ; the asymptotic continuous solution of the system of parabolic quasi-variational inequalities with noncoercive operators. The proof uses an algorithmic approach and the system of elliptic quasi-variational inequalities results.

Allan-Cahn and Cahn-Hilliard variational inequalities solved with Optimization Techniques

Parabolic variational inequalities of Allen-Cahn and CahnHilliard type are solved using methods involving constrained optimization. Time discrete variants are formulated with the help of Lagrange multipliers for local and non-local equality and inequality constraints. Fully discrete problems resulting from finite element discretizations in space are solved with the help of a primal-dual active ...

Ergodicity of Robust Switching Control and Nonlinear System of Quasi-Variational Inequalities

We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities. These equations are related to robust switching control problems introduced in [6]. We prove that, as time horizon goes to infinity (resp. discount factor goes to zero) the long run average solution to the parabolic system (resp. the limiting discounted solution to the ellip...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

On Noncoercive Variational Inequalities

We consider variational inequalities with different trial and test spaces and a possibly non-coercive bilinear form. Well-posedness is shown under general conditions that are e.g. valid for the space-time variational formulation of parabolic variational inequalities. Moreover, we prove an estimate for the error of a Petrov-Galerkin approximation in terms of the residual. For parabolic variation...