Spherical Symmetrization and Eigenvalue Estimates.
Stability of a variational inequality with respect to domain perturbations.
Stability of eigenvalues and eigenvectors of variational inequalities
Stability of Noor iterations with errors for generalized nonlinear complementarity problems.
Stability results for obstacle problems with measure data
Stable approximations of a minimal surface problem with variational inequalities.
Stable evaluation of differential operators and linear and nonlinear multi-scale filtering.
Star shaped coincidence sets in the obstacle problem
Steady Boussinesq system with mixed boundary conditions including friction conditions
In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution...
Strong convergence for generalized equilibrium problems, fixed point problems and relaxed cocoercive variational inequalities.
Strong convergence of a hybrid projection algorithm for equilibrium problems, variational inequality problems and fixed point problems in a Banach space.
Strong convergence of a modified iterative algorithm for mixed-equilibrium problems in Hilbert spaces.
Strong convergence of an iterative method for equilibrium problems and variational inequality problems.
Strong convergence of an iterative method for inverse strongly accretive operators.
Strong convergence theorem for a new general system of variational inequalities in Banach spaces.
Study of a contact problem with normal compliance and nonlocal friction
We consider a static frictional contact between a nonlinear elastic body and a foundation. The contact is modelled by a normal compliance condition such that the penetration is restricted with unilateral constraint and associated to the nonlocal friction law. We derive a variational formulation and prove its unique weak solvability if the friction coefficient is sufficiently small. Moreover, we prove the continuous dependence of the solution on the contact conditions. Also we study the finite element...
Study of a viscoelastic frictional contact problem with adhesion
We consider a quasistatic frictional contact problem between a viscoelastic body with long memory and a deformable foundation. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral constraint. The adhesion between contact surfaces is taken into account and the evolution of the bonding field is described by a first order differential equation. We derive a variational formulation and prove the existence and uniqueness result of the...
Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems
We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...
Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities
* This work was completed while the author was visiting the University of Limoges. Support from the laboratoire “Analyse non-linéaire et Optimisation” is gratefully acknowledged.The author recently introduced a regularity assumption for derivatives of set-valued mappings, in order to obtain first order necessary conditions of optimality, in some generalized sense, for nondifferentiable control problems governed by variational inequalities. It was noticed that this regularity assumption can be...
Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities
In this paper sufficient second order optimality conditions for optimal control problems subject to stationary variational inequalities of obstacle type are derived. Since optimality conditions for such problems always involve measures as Lagrange multipliers, which impede the use of efficient Newton type methods, a family of regularized problems is introduced. Second order sufficient optimality conditions are derived for the regularized problems...