Optimal Control of Quasivariational Inequalities with Applications to Contact Mechanics

2019 ◽  
pp. 445-489 ◽  
Author(s):  
Mircea Sofonea
Keyword(s):  
Optimal Control ◽  
Contact Mechanics ◽  
Quasivariational Inequalities

Differential quasivariational inequalities in contact mechanics

2018 ◽  
Vol 24 (3) ◽  
pp. 845-861 ◽  
Author(s):  
Zhenhai Liu ◽  
Mircea Sofonea
Keyword(s):  
Contact Mechanics ◽  
Contact Problems ◽  
Quasivariational Inequality ◽  
Quasivariational Inequalities ◽  
Abstract Result ◽  
New Class ◽  
Physical Setting ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Weak Solvability

We consider a new class of differential quasivariational inequalities, i.e. a nonlinear system that couples a differential equation with a time-dependent quasivariational inequality, both defined on abstract Banach spaces. We state and prove a general fixed principle that provides the existence and the uniqueness of the solution of the system. Then we consider a relevant particular setting for which our abstract result holds. We proceed with two examples that arise in Contact Mechanics. For each example, we describe the physical setting, the mathematical model and the assumption on the data. Then we state the variational formulation of each model, which is in the form of a differential quasivariational inequality. Finally, we apply our abstract results to provide the unique weak solvability of the corresponding contact problems.

scholarly journals A class of parabolic evolutionary quasivariational inequalities in contact mechanics

2020 ◽  
Vol 36 (1) ◽  
pp. 45-47
Author(s):  
CHEN TAO ◽  
HUANG NAN-JING ◽  
XIAO YI-BIN
Keyword(s):  
Contact Mechanics ◽  
Existence And Uniqueness ◽  
Quasivariational Inequality ◽  
Quasivariational Inequalities ◽  
Mild Conditions ◽  
Element Free Galerkin ◽  
Uniqueness Of The Solution ◽  
Spatial Approximation ◽  
Element Free ◽  
Forward Euler

In this paper, we obtain an existence and uniqueness of the solution for a class of parabolic evolutionary quasivariational inequalities in contact mechanics under some mild conditions. We also study an error estimate for the parabolic evolutionary quasivariational inequality by employing the forward Euler difference scheme and the element-free Galerkin spatial approximation.

Sign in / Sign up

Export Citation Format

Share Document