A class of elliptic quasi-variational-hemivariational inequalities with applications

In this paper we study a class of quasi--variational--hemi\-va\-ria\-tio\-nal inequalities in reflexive Banach spaces. The inequalities contain a convex potential, a locally Lipschitz superpotential, and a solution-dependent set of constraints. Solution existence and compactness of the solution set to the inequality problem are established based on the Kakutani--Ky Fan--Glicksberg fixed point theorem. Two examples of the interior and boundary semipermeability models illustrate the applicability of our results.Comment: 15

A new class of history-dependent quasi variational-hemivariational inequalities with constraints

In this paper we consider an abstract class of time-dependent quasi variational-hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of solution by using a recent result for elliptic variational-hemivariational inequalities in reflexive Banach spaces combined with a fixed-point principle for history-dependent operators. Then, we apply the abstract result to show the unique weak solvability to a quasistatic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity and the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated slip.Comment: 15

Existence of solution to a new class of coupled variational-hemivariational inequalities

The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We establish the nonemptiness and compactness of the solution set to the system. We apply a new method of proof based on a multivalued version of the Tychonoff fixed point principle in a Banach space combined with the generalized monotonicity arguments, and elements of the nonsmooth analysis. Our results improve and generalize some earlier theorems obtained for a very particular form of the system.Comment: 17

A model of a spring-mass-damper system with temperature-dependent friction

International audienceThis work models and analyses the dynamics of a general spring-mass-damper system that is in frictional contact with its support, taking into account frictional heat generation and a reactive obstacle. Friction, heat generation and contact are modelled with subdifferentials of, possibly non-convex, potential functions. The model consists of a non-linear system of first-order differential inclusions for the position, velocity and temperature of the mass. The existence of a global solution is established and additional assumptions yield its uniqueness. Nine examples of conditions arising in applications, for which the analysis results are valid, are presented