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2848. Existence results for coupled systems of variational inequalities
Invited abstract in session WD-43: Recent advances on Variational Inequalities and Equilibrium Problems III , stream Variational Inequalities and Equilibrium Problems: From Theoretical Advances to Real World Applications.
Wednesday, 14:30-16:00Room: 99 (building: 306)
Authors (first author is the speaker)
| 1. | Nicusor Costea
|
| Mathematics and Computer Science, Politehnica National University of Science and Technology Bucharest |
Abstract
In this talk the existence of solutions for a system consisting of two inequalities of variational type is discussed. Each inequality is formulated in terms of a nonlinear bifunction and a coupling functional. We consider two sets of assumptions for each of the functional involved in the formulation of the system and show that if the constraint sets are nonempty, closed, convex and bounded then the system possesses at least one solution regardless of the assumption imposed on each functional. If one of the constraint sets is unbounded, then a coercivity condition is needed to ensure the existence of solutions. We provide two such conditions.
The theoretical results are then employed to establish the existence of weak solutions for a mathematical model which describes the antiplane shear deformation of a cylinder made of a nonlinear elastic material and a rigid foundation.
Keywords
- Convex Optimization
- Non-smooth Optimization
Status: accepted
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