scholarly journals Lipschitz perturbation to evolution inclusion driven by time-dependent maximal monotone operators

2021 ◽  
pp. 1-36
Author(s):  
Charles Castaing ◽  
Soumia Saïdi
Keyword(s):  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Time Dependent ◽  
Evolution Inclusion ◽  
Lipschitz Perturbation

scholarly journals Multi-valued perturbation to evolution problems involving time dependent maximal monotone operators

2020 ◽  
Vol 9 (1) ◽  
pp. 219-254 ◽  
Author(s):  
Dalila Azzam-Laouir ◽  
◽  
Warda Belhoula ◽  
Charles Castaing ◽  
M. D. P. Monteiro Marques ◽  
...  
Keyword(s):  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Time Dependent ◽  
Evolution Problems

scholarly journals Hidden maximal monotonicity in evolutionary variational-hemivariational inequalities

2021 ◽  
Vol 26 (6) ◽  
pp. 1144-1165
Author(s):  
Emilio Vilches ◽  
Shengda Zeng
Keyword(s):  
Evolution Equations ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Evolution Inclusion ◽  
Theory Of Evolution ◽  
Maximal Monotonicity ◽  
Theoretical Results

In this paper, we propose a new methodology to study evolutionary variational-hemivariational inequalities based on the theory of evolution equations governed by maximal monotone operators. More precisely, the proposed approach, based on a hidden maximal monotonicity, is used to explore the well-posedness for a class of evolutionary variational-hemivariational inequalities involving history-dependent operators and related problems with periodic and antiperiodic boundary conditions. The applicability of our theoretical results is illustrated through applications to a fractional evolution inclusion and a dynamic semipermeability problem.

scholarly journals Topological degree and application to a parabolic variational inequality problem

2001 ◽  
Vol 25 (4) ◽  
pp. 273-287 ◽  
Author(s):  
A. Addou ◽  
B. Mermri
Keyword(s):  
Variational Inequality ◽  
Topological Degree ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Parabolic Variational Inequality ◽  
Inequality Problem ◽  
Monotone Map ◽  
New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

scholarly journals Theoretical Study of a Chain Sliding on a Fixed Support

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
Jérôme Bastien ◽  
Claude-Henri Lamarque
Keyword(s):  
Dry Friction ◽  
Theoretical Study ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Rheological Models ◽  
Implicit Euler Scheme ◽  
Linear Spring ◽  
A Chain ◽  
Uniqueness Theory

A chain sliding on a fixed support, made out of some elementary rheological models (dry friction element and linear spring) can be covered by the existence and uniqueness theory for maximal monotone operators. Several behavior from quasistatic to dynamical are investigated. Moreover, classical results of numerical analysis allow to use a numerical implicit Euler scheme.

Generalized relaxed inertial method with regularization for solving split feasibility problems in real Hilbert spaces

2021 ◽  
pp. 2250106
Author(s):  
A. A. Mebawondu ◽  
L. O. Jolaoso ◽  
H. A. Abass ◽  
O. K. Narain
Keyword(s):  
Hilbert Spaces ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Split Feasibility Problem ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Inertial Method ◽  
Split Feasibility

In this paper, we propose a new modified relaxed inertial regularization method for finding a common solution of a generalized split feasibility problem, the zeros of sum of maximal monotone operators, and fixed point problem of two nonlinear mappings in real Hilbert spaces. We prove that the proposed method converges strongly to a minimum-norm solution of the aforementioned problems without using the conventional two cases approach. In addition, we apply our convergence results to the classical variational inequality and equilibrium problems, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other existing methods in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

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