Continuous Dependence and Optimal Control for a Class of Variational–Hemivariational Inequalities

Jiang, Caijing; Zeng, Biao

doi:10.1007/s00245-018-9543-4

Cited by 7 publications

(2 citation statements)

References 16 publications

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“…Numerical analysis of variational inequalities, including solution algorithms, error estimates and numerical simulations, can be found in [4,8,10,23,25]. Some results on optimal control of variational inequalities can be found in [5,11,14,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

A regularized frictional contact problem with unilateral constraints

Benraouda

2024

EJMCA

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We consider a mathematical model which describes the equilibrium of an elastic body in contact with a deformable foundation. We describe the contact model and we establish the existence of a unique weak solution to the problem. Then, we prove the continuous dependence of the solution with respect to the data. Finally, we introduce a sequence of regularized problems depending on a positive parameter for which we study the convergence when the regularization parameter is very small.

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Section: Introductionmentioning

confidence: 99%

A regularized frictional contact problem with unilateral constraints

Benraouda

2024

EJMCA

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“…Literature in this field for static contact models can be found in e.g. [31,28,15,8,25] with elastic or piezoelectric materials. For dynamic contact models, since the discussion is more challenging, publications are limited, see [11,23,19,7] with viscoelastic or thermoviscoelastic materials.…”

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confidence: 99%

Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

Wang

Cheng

2022

EECT

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<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>

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The Zero Duality Gap Property for an Optimal Control Problem Governed by a Multivalued Hemivariational Inequality

Fengzhen

Zeng

2020

Appl Math Optim

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Continuous Dependence and Optimal Control for a Class of Variational–Hemivariational Inequalities

Cited by 7 publications

References 16 publications

A regularized frictional contact problem with unilateral constraints

A regularized frictional contact problem with unilateral constraints

Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

The Zero Duality Gap Property for an Optimal Control Problem Governed by a Multivalued Hemivariational Inequality

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