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Tykhonov well-posedness of a mixed variational problem.
- Source :
-
Optimization . Mar2022, Vol. 71 Issue 3, p561-581. 21p. - Publication Year :
- 2022
-
Abstract
- We consider a mixed variational problem governed by a nonlinear operator and a set of constraints. Existence, uniqueness and convergence results for this problem have already been obtained in the literature. In this current paper we complete these results by proving the well-posedness of the problem, in the sense of Tykhonov. To this end we introduce a family of approximating problems for which we state and prove various equivalence and convergence results. We illustrate these abstract results in the study of a frictionless contact model with elastic materials. The process is assumed to be static and the contact is with unilateral constraints. We derive a weak formulation of the model which is in the form of a mixed variational problem with unknowns being the displacement field and the Lagrange multiplier. Then, we prove various results on the corresponding mixed problem, including its well-posedness in the sense of Tykhonov, under various assumptions on the data. Finally, we provide mechanical interpretation of our results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONLINEAR operators
*LAGRANGE multiplier
*NONLINEAR equations
Subjects
Details
- Language :
- English
- ISSN :
- 02331934
- Volume :
- 71
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 156075278
- Full Text :
- https://doi.org/10.1080/02331934.2020.1808646