On the solvability of mixed variational problems with solution-dependent sets of Lagrange multipliers

Matei, Andaluzia

doi:10.1017/s0308210512000637

Cited by 11 publications

(6 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof of Theorem 2, based on the abstract results we have got in [11], can be found in the very recent paper [12]. Remark 1.…”

Section: On the Weak Solvability Of The Modelmentioning

confidence: 99%

On the Weak Solvability and the Optimal Control of a Frictional Contact Problem with Normal Compliance

Matei

2016

IFIP Advances in Information and Communication Technology

Self Cite

View full text Add to dashboard Cite

In the present work we consider a frictional contact model with normal compliance. Firstly, we discuss the weak solvability of the model by means of two variational approaches. In a first approach the weak solution is a solution of a quasivariational inequality. In a second approach the weak solution is a solution of a mixed variational problem with solution-dependent set of Lagrange multipliers. Nextly, the paper focuses on the boundary optimal control of the model. Existence results, an optimality condition and some convergence results are presented.

show abstract

“…The proof of Theorem 2, based on the abstract results we have got in [11], can be found in the very recent paper [12]. Remark 1.…”

Section: On the Weak Solvability Of The Modelmentioning

confidence: 99%

On the Weak Solvability and the Optimal Control of a Frictional Contact Problem with Normal Compliance

Matei

2016

IFIP Advances in Information and Communication Technology

Self Cite

View full text Add to dashboard Cite

show abstract

“…Also, by (55) the bilinear form e (·, ·) defined in (63) verifies Assumption 3 with M e = ‖ μ ‖ L ∞ ( Ω ) and m e = μ *. To prove that the bilinear form b (·, ·) verifies Assumption 4, arguments similar to those used in [6, 24] can be used; for the convenience of the reader, we shall indicate below the justification. First,…”

Section: A Frictional Contact Problemmentioning

confidence: 99%

An evolutionary mixed variational problem arising from frictional contact mechanics

Matei

2012

Mathematics and Mechanics of Solids

Self Cite

View full text Add to dashboard Cite

We consider an abstract mixed variational problem which consists of a system of an evolutionary variational equation in a Hilbert space X and an evolutionary inequality in a subset of a second Hilbert space Y , associated with an initial condition. The existence and the uniqueness of the solution is proved based on a fixed point technique. The continuous dependence on the data was also investigated. The abstract results we obtain can be applied to the mathematical treatment of a class of frictional contact problems for viscoelastic materials with short memory. In this paper we consider an antiplane model for which we deliver a mixed variational formulation with friction bound dependent set of Lagrange multipliers. After proving the existence and the uniqueness of the weak solution, we study the continuous dependence on the initial data, on the densities of the volume forces and surface tractions. Moreover, we prove the continuous dependence of the solution on the friction bound. KeywordsEvolutionary mixed variational problem, saddle point, fixed point, friction bound dependent set, dual Lagrange multipliers, weak solutions, continuous dependence on the data, viscoelasticity, frictional contact problems

show abstract

“…Considering such kinds of variational problems sets the functional background in the study of elastic contact problems with unilateral constraints and nonmonotone interface laws. For very recent work, see [ 1 – 3 ]. Our results improve the results in [ 4 – 7 ], which consider a bilinear functional.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness result for a class of mixed variational problems

Jiang

2018

J Inequal Appl

View full text Add to dashboard Cite

show abstract

On the solvability of mixed variational problems with solution-dependent sets of Lagrange multipliers

Cited by 11 publications

References 11 publications

On the Weak Solvability and the Optimal Control of a Frictional Contact Problem with Normal Compliance

On the Weak Solvability and the Optimal Control of a Frictional Contact Problem with Normal Compliance

An evolutionary mixed variational problem arising from frictional contact mechanics

Existence and uniqueness result for a class of mixed variational problems

Contact Info

Product

Resources

About