Open Access
Translator Disclaimer
2013 Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities
J. Gwinner
Abstr. Appl. Anal. 2013(SI51): 1-10 (2013). DOI: 10.1155/2013/108043

Abstract

The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.

Citation

Download Citation

J. Gwinner. "Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities." Abstr. Appl. Anal. 2013 (SI51) 1 - 10, 2013. https://doi.org/10.1155/2013/108043

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1277.35183
MathSciNet: MR3049426
Digital Object Identifier: 10.1155/2013/108043

Rights: Copyright © 2013 Hindawi

JOURNAL ARTICLE
10 PAGES


SHARE
Vol.2013 • No. SI51 • 2013
Back to Top