Convergence of a generalized penalty method for variational–hemivariational inequalities

Zeng, Shengda; Migórski, Stanisław; Liu, Zhenhai; Yao, Jen‐Chih

doi:10.1016/j.cnsns.2020.105476

Cited by 34 publications

(20 citation statements)

References 28 publications

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“…It is well known that the penalty method is a kind of efficient approximating method forvarious problems. It is also constantly used for the study of VIs and HVIs (see, for example, [3,21,28,31]). Due to the close relationship with VIs and HVIs, differential variational inequalities (DVIs) and differential hemivariational inequalities (DHVIs) are studied by employing the penalty method, such as Liu and Zeng [16,17] and Weng et al [27].…”

Section: W(t) U(t))mentioning

confidence: 99%

Penalty method for a class of differential nonlinear system arising in contact mechanics

Chu

Chen

Huang

et al. 2022

Fixed Point Theory Algorithms Sci Eng

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The main goal of this paper is to study a class of differential nonlinear system involving parabolic variational and history-dependent hemivariational inequalities in Banach spaces by using the penalty method. We first construct a penalized problem for such a nonlinear system and then derive the existence and uniqueness of its solution to obtain an approximating sequence for the nonlinear system. Moreover, we prove the strong convergence of the obtained approximating sequence to the solution of the original nonlinear system when the penalty parameter converges to zero. Finally, we apply the obtained convergence result to a long-memory elastic frictional contact problem with wear and damage in mechanics. First part title: Introduction Second part title: Preliminaries Third part title: Convergence result for (1.1) Fourth part title: An application

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Section: W(t) U(t))mentioning

confidence: 99%

Penalty method for a class of differential nonlinear system arising in contact mechanics

Chu

Chen

Huang

et al. 2022

Fixed Point Theory Algorithms Sci Eng

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“…In the past few years, several types of variational and hemivariational inequalities have been developed and the study of variational-hemivariational inequalities has emerged today as a new, noble, innovative and interesting branch of applied and industrial mathematics, see [2,18,19,25,26,27,28,29,30,31,33,34,35,36]. The problem of generalized mixed variational-hemivariational inequality problem demonstrated in this work as follows: Let (V, ∥•∥ V ) and (X, ∥•∥ X ) be reflexive and separable Banach spaces, and ℧ be a nonempty closed convex subset of V. V * denotes the dual space of V and ⟨•, •⟩ be the duality pairing between V * and V. Given the mappings N : V × V → V * , J : X → R, φ :…”

Section: Introductionmentioning

confidence: 99%

"The penalty method for generalized mixed variational-hemivariational inequality problems"

Chang¹,

Salahuddin²,

Ahmadini³

et al. 2022

CJM

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"It is well known that many popular variational, quasi-variational, hemivariational inequalities and variational inclusions involving constraints in a Banach space to convert a fixed point problems for finding the solution of such problems. This paper is to infuse a sequence of penalized problems without constraints and we show under the few reasonable assumptions to the Kuratowski upper limit with respect to the weak topology of the sets of solutions to penalized problems is nonempty. As an application, we explore two complicated partial differential systems of elliptic mixed boundary value problem involving a nonlinear nonhomogeneous differential operator with an obstacle effect, and a nonlinear elastic contact problem in mechanics with unilateral constraints."

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“…Hemivariational inequalities have important applications in mechanics and engineering, especially in nonsmooth analysis and optimization; see, e.g., [1,2,3]. In recent years, under various assumptions, the existence theorems and well-posedness results for hemivariational inequalities have been proven by many authors; see, e.g., [4,5,6,7] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On approximate controllability for systems of fractional evolution hemivariational inequalities with Riemann-Liouville fractional derivatives

2022

J. Nonlinear Var. Anal.

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In this paper, we deal with the control systems governed by the systems of fractional evolution hemivariational inequalities involving Riemann-Liouville fractional derivatives. We establish suitable sufficient conditions to guarantee the existence of mild solutions. Under these conditions, the approximate controllability of the associated fractional evolution systems involving Riemann-Liouville fractional derivatives is formulated and proved.

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Convergence of a generalized penalty method for variational–hemivariational inequalities

Cited by 34 publications

References 28 publications

Penalty method for a class of differential nonlinear system arising in contact mechanics

Penalty method for a class of differential nonlinear system arising in contact mechanics

"The penalty method for generalized mixed variational-hemivariational inequality problems"

On approximate controllability for systems of fractional evolution hemivariational inequalities with Riemann-Liouville fractional derivatives

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