scholarly journals A General Class of Differential Hemivariational Inequalities Systems in Reflexive Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3173
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen ◽  
Yeong-Cheng Liou ◽  
Jen-Chih Yao
Keyword(s):  
Evolution Equations ◽  
Recent Literature ◽  
Type System ◽  
Parabolic Type ◽  
Hemivariational Inequalities ◽  
Product Spaces ◽  
Reflexive Banach Spaces ◽  
Evolution Triple ◽  
Iterative System ◽  
Subgradient Mappings

We consider an abstract system consisting of the parabolic-type system of hemivariational inequalities (SHVI) along with the nonlinear system of evolution equations in the frame of the evolution triple of product spaces, which is called a system of differential hemivariational inequalities (SDHVI). A hybrid iterative system is proposed via the temporality semidiscrete technique on the basis of the Rothe rule and feedback iteration approach. Using the surjective theorem for pseudomonotonicity mappings and properties of the partial Clarke’s generalized subgradient mappings, we establish the existence and priori estimations for solutions to the approximate problem. Whenever studying the parabolic-type SHVI, the surjective theorem for pseudomonotonicity mappings, instead of the KKM theorems exploited by other authors in recent literature for a SHVI, guarantees the successful continuation of our demonstration. This overcomes the drawback of the KKM-based approach. Finally, via the limitation process for solutions to the hybrid iterative system, we derive the solvability of the SDHVI with no convexity of functions u↦fl(t,x,u),l=1,2 and no compact property of C0-semigroups eAl(t),l=1,2.

scholarly journals A Class of Variational-Hemivariational Inequalities in Reflexive Banach Spaces

2016 ◽  
Vol 127 (2) ◽  
pp. 151-178 ◽  
Author(s):  
Stanisław Migórski ◽  
Anna Ochal ◽  
Mircea Sofonea
Keyword(s):  
Banach Spaces ◽  
Hemivariational Inequalities ◽  
Reflexive Banach Spaces

scholarly journals A new class of hyperbolic variational–hemivariational inequalities driven by non-linear evolution equations

2020 ◽  
Vol 32 (1) ◽  
pp. 59-88
Author(s):  
STANISŁAW MIGÓRSKI ◽  
WEIMIN HAN ◽  
SHENGDA ZENG
Keyword(s):  
Dynamical System ◽  
Evolution Equations ◽  
Frictional Contact ◽  
Maximal Monotone ◽  
Contact Boundary ◽  
Hemivariational Inequalities ◽  
Response Condition ◽  
Linear Evolution ◽  
Linear Evolution Equation ◽  
Non Linear

The aim of the paper is to introduce and investigate a dynamical system which consists of a variational–hemivariational inequality of hyperbolic type combined with a non-linear evolution equation. Such a dynamical system arises in studies of complicated contact problems in mechanics. Existence, uniqueness and regularity of a global solution to the system are established. The approach is based on a new semi-discrete approximation with an application of a surjectivity result for a pseudomonotone perturbation of a maximal monotone operator. A new dynamic viscoelastic frictional contact model with adhesion is studied as an application, in which the contact boundary condition is described by a generalised normal damped response condition with unilateral constraint and a multivalued frictional contact law.

scholarly journals Partial differential hemivariational inequalities

2018 ◽  
Vol 7 (4) ◽  
pp. 571-586 ◽  
Author(s):  
Zhenhai Liu ◽  
Shengda Zeng ◽  
Dumitru Motreanu
Keyword(s):  
Evolution Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Upper Semicontinuity ◽  
Solution Set ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Partial Differential ◽  
New Class

AbstractThe aim of this paper is to introduce and study a new class of problems called partial differential hemivariational inequalities that combines evolution equations and hemivariational inequalities. First, we introduce the concept of strong well-posedness for mixed variational quasi hemivariational inequalities and establish metric characterizations for it. Then we show the existence of solutions and meaningful properties such as measurability and upper semicontinuity for the solution set of the mixed variational quasi hemivariational inequality associated to the partial differential hemivariational inequality. Relying, on these properties we are able to prove the existence of mild solutions for partial differential hemivariational inequalities. Furthermore, we show the compactness of the set of the corresponding mild trajectories.

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