scholarly journals Impulsive hemivariational inequality for a class of history-dependent quasistatic frictional contact problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Furi Guo ◽  
Jinrong Wang ◽  
Jiangfeng Han
Keyword(s):  
Differential Equation ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Impulsive Differential Equation ◽  
Frictional Contact ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Pseudomonotone Operator ◽  
Weak Formulation ◽  
Uniqueness Results

<p style='text-indent:20px;'>This paper deals with a class of history-dependent frictional contact problem with the surface traction affected by the impulsive differential equation. The weak formulation of the contact problem is a history-dependent hemivariational inequality with the impulsive differential equation. By virtue of the surjectivity of multivalued pseudomonotone operator theorem and the Rothe method, existence and uniqueness results on the abstract impulsive differential hemivariational inequalities is established. In addition, we consider the stability of the solution to impulsive differential hemivariational inequalities in relation to perturbation data. Finally, the existence and uniqueness of weak solution to the contact problem is proved by means of abstract results.</p>

Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Zakaria Faiz ◽  
Driss El Moutawakil
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Frictional Contact ◽  
Hemivariational Inequalities ◽  
Frictional Contact Problem ◽  
Uniqueness Of A Solution

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

scholarly journals A new class of fractional impulsive differential hemivariational inequalities with an application

2022 ◽  
Vol 27 ◽  
pp. 1-22
Author(s):  
Yun-hua Weng ◽  
Tao Chen ◽  
Nan-jing Huang ◽  
Donal O'Regan
Keyword(s):  
Differential Equation ◽  
Impulsive Differential Equation ◽  
Convergence Result ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
New Class ◽  
Perturbation Problem ◽  
Perturbation Data ◽  
The Stability ◽  
Stability Of The Solution

We consider a new fractional impulsive differential hemivariational inequality, which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework. By utilizing a surjectivity theorem and a fixed point theorem we establish an existence and uniqueness theorem for such a problem. Moreover, we investigate the perturbation problem of the fractional impulsive differential hemivariational inequality to prove a convergence result, which describes the stability of the solution in relation to perturbation data. Finally, our main results are applied to obtain some new results for a frictional contact problem with the surface traction driven by the fractional impulsive differential equation.

scholarly journals Existence and Uniqueness of Solutions for Coupled Impulsive Fractional Pantograph Differential Equations with Antiperiodic Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Karim Guida ◽  
Lahcen Ibnelazyz ◽  
Khalid Hilal ◽  
Said Melliani
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based on Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Two examples are given in the last part to support our study.

scholarly journals Existence and Uniqueness with Ulam Stability study of the solution for a class of Caputo fractional integro-differential equation with mixed conditions

2021 ◽  
Author(s):  
ABDELLOUAHAB Naimi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Stability Study ◽  
Ulam Stability ◽  
Differential Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Stability Results

In this article we show the existence, uniqueness and Ulam stability results of the solution for a class of a nonlinear Caputo fractional integro-differential problem with mixed conditions. we use three fixed point theorems to proof the existence and uniqueness results. By the results obtained, the reasons for the Ulam stability are verified. An example proposed to illustrate our main results.

Hemivariational inverse problem for contact problem with locking materials

2021 ◽  
Vol 8 (4) ◽  
pp. 665-677
Author(s):  
Z. Faiz ◽  
◽  
O. Baiz ◽  
H. Benaissa ◽  
D. El Moutawakil ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Contact Problem ◽  
Frictional Contact ◽  
Deformable Body ◽  
Lipschitz Mapping ◽  
Hemivariational Inequalities ◽  
Existence Of A Solution ◽  
Locally Lipschitz ◽  
Uniqueness Of The Solution ◽  
Dependence Result

The aim of this work is to study an inverse problem for a frictional contact model for locking material. The deformable body consists of electro-elastic-locking materials. Here, the locking character makes the solution belong to a convex set, the contact is presented in the form of multivalued normal compliance, and frictions are described with a sub-gradient of a locally Lipschitz mapping. We develop the variational formulation of the model by combining two hemivariational inequalities in a linked system. The existence and uniqueness of the solution are demonstrated utilizing recent conclusions from hemivariational inequalities theory and a fixed point argument. Finally, we provided a continuous dependence result and then we established the existence of a solution to an inverse problem for piezoelectric-locking material frictional contact problem.

Approximation of Thermoelasticity Frictional Contact Problem with Hemivariational Inequality

2009 ◽  
Author(s):  
Ivan Šestak ◽  
Boško S. Jovanović ◽  
George Venkov ◽  
Ralitza Kovacheva ◽  
Vesela Pasheva
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Hemivariational Inequality ◽  
Frictional Contact Problem
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