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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 108043, 10 pages
Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities
Institut für Mathematik und Rechneranwendung, Universität der Bundeswehr München, 85577 Neubiberg/München, Germany
Received 29 December 2012; Accepted 15 March 2013
Academic Editor: Donal O'Regan
Copyright © 2013 J. Gwinner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- G. N. Gatica, “An application of Babuška-Brezzi's theory to a class of variational problems,” Applicable Analysis, vol. 75, no. 3-4, pp. 297–303, 2000.
- G. N. Gatica, “Solvability and Galerkin approximations of a class of nonlinear operator equations,” Zeitschrift für Analysis und ihre Anwendungen, vol. 21, no. 3, pp. 761–781, 2002.
- G. N. Gatica, N. Heuer, and S. Meddahi, “On the numerical analysis of nonlinear twofold saddle point problems,” IMA Journal of Numerical Analysis, vol. 23, no. 2, pp. 301–330, 2003.
- I. Ekeland and R. Temam, Analyse Convexe et Problèmes Variationnels, Dunod, Gauthier-Villars, Paris, France, 1974.
- J. Haslinger, “Mixed formulation of elliptic variational inequalities and its approximation,” Aplikace Matematiky, vol. 26, no. 6, pp. 462–475, 1981.
- J. Haslinger and J. Lovíšek, “Mixed variational formulation of unilateral problems,” Commentationes Mathematicae Universitatis Carolinae, vol. 21, no. 2, pp. 231–246, 1980.
- I. Hlaváček, J. Haslinger, J. Nečas, and J. Lovíšek, Numerical Solution of Variational Inequalities, vol. 66 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1988.
- J.-S. Pang and D. E. Stewart, “Differential variational inequalities,” Mathematical Programming, vol. 113, no. 2, pp. 345–424, 2008.
- X.-S. Li, N.-J. Huang, and D. O'Regan, “Differential mixed variational inequalities in finite dimensional spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 9-10, pp. 3875–3886, 2010.
- D. Goeleven, D. Motreanu, and V. V. Motreanu, “On the stability of stationary solutions of first order evolution variational inequalities,” Advances in Nonlinear Variational Inequalities, vol. 6, no. 1, pp. 1–30, 2003.
- J.-S. Pang and D. E. Stewart, “Solution dependence on initial conditions in differential variational inequalities,” Mathematical Programming, vol. 116, no. 1-2, pp. 429–460, 2009.
- N. S. Papageorgiou, “A stability result for differential inclusions in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 118, no. 1, pp. 232–246, 1986.
- N. S. Papageorgiou, “On parametric evolution inclusions of the subdifferential type with applications to optimal control problems,” Transactions of the American Mathematical Society, vol. 347, no. 1, pp. 203–231, 1995.
- S. Hu and N. S. Papageorgiou, “Time-dependent subdifferential evolution inclusions and optimal control,” Memoirs of the American Mathematical Society, vol. 133, no. 632, 81 pages, 1998.
- D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, vol. 88 of Pure and Applied Mathematics, Academic Press, New York, NY, USA, 1984.
- E. Zeidler, “Nonlinear Monotone Operators,” in Nonlinear Functional Analysis and Its Applications, part 2, Springer, New York, NY, USA, 1990.
- J. Gwinner, “On differential variational inequalities and projected dynamical systems—equivalence and a stability result,” Discrete and Continuous Dynamical Systems A, vol. 2007, pp. 467–476, 2007.
- J. Gwinner, “A note on linear differential variational inequalities in Hilbert space,” in Modeling and Optimization, D. Hömberg and F. Tröltzsch, Eds., pp. 85–91, Springer, Heidelberg, Germany, 2013.
- H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Clarendon, New York, NY, USA, 2nd edition, 1988.
- G. Duvaut and J.-L. Lions, Inequalities in Mechanics and Physics, Springer, Berlin, Germany, 1976.
- J. Nečas, Les Méthodes Directes en Théorie des Équations Elliptiques, Masson, Paris, France, 1967.
- V. Girault and P.-A. Raviart, Finite Element Approximation of the Navier-Stokes Equations, vol. 749 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1981.
- R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol. 5, Springer, Berlin, Germany, 1992.
- M. Kunze, Non-Smooth Dynamical Systems, vol. 1744 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2000.
- H. Attouch, Variational Convergence for Functions and Operators, Applicable Mathematics Series, Pitman, Boston, Mass, USA, 1984.
- J. Gwinner, “A class of random variational inequalities and simple random unilateral boundary value problems–-existence, discretization, finite element approximation,” Stochastic Analysis and Applications, vol. 18, no. 6, pp. 967–993, 2000.
- J. Gwinner, “Stability of monotone variational inequalities with various applications,” in Variational Inequalities and Network Equilibrium Problems, F. Giannessi and A. Maugeri, Eds., pp. 123–142, Plenum, New York, NY, USA, 1995.
- G. Beer and J. M. Borwein, “Mosco convergence and reflexivity,” Proceedings of the American Mathematical Society, vol. 109, no. 2, pp. 427–436, 1990.
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, vol. 15 of Springer Series in Computational Mathematics, Springer, New York, NY, USA, 1991.
- K. Deimling, Multivalued Differential Equations, vol. 1 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, Germany, 1992.
- J.-P. Aubin and A. Cellina, Differential Inclusions, vol. 264 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Germany, 1984.
- R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer Series in Computational Physics, Springer, New York, NY, USA, 1984.
- C. Carstensen and J. Gwinner, “A theory of discretization for nonlinear evolution inequalities applied to parabolic Signorini problems,” Annali di Matematica Pura ed Applicata, vol. 177, pp. 363–394, 1999.