Abstract
We propose an iterative algorithm for solving a semicoercive nonsmooth variational inequality. The algorithm is based on the stepwise partial smoothing of the minimized functional and an iterative proximal regularization method.
We obtain a solution to the variational Mosolov and Myasnikov problem with boundary friction as a limit point of a sequence of solutions to stable auxiliary problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Ya. Zolotukhin, R. V. Namm, and A. V. Pachina, “Approximate Solution of the Mosolov and Myasnikov Problem with the Coulomb Boundary Friction,” Sib. Zhurn. Vychisl. Matem. 4(2), 163–177 (2001).
P. P. Mosolov and V. P. Myasnikov, “On Qualitative Singularities of the Flow of a Viscous-Plastic Medium in Pipes,” Zhurn. Prikl. Matem. iMekh. 31(3), 581–585 (1967).
H. Schmitt, “On the Regularized Bingham Problem,” Lecture Notes Econ. Math. Syst. (Springer-Verlag, Berlin, 1997), Vol. 452, pp. 298–315.
E. M. Vikhtenko and R. V. Namm, “Solution Method for Semicoercive Variational Inequalities Based on the Method of Iterative Proximal Regularization,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 1, 31–35 (2004) [RussianMathematics (Iz. VUZ) 48 (1), 28–32 (2004)].
G. I. Marchuk and V. I. Agoshkov, Introduction to Projection-Grid Methods (Nauka, Moscow, 1981) [in Russian].
A. Ya. Zolotukhin, R. V. Namm, and A. V. Pachina, “Approximate Solution to the Semicoercive Signorini Problem with Nonhomogeneous Boundary Conditions,” Zhurn. Vyssh. Matem. i Matem. Fiz. 43(3), 388–398 (2003).
R. V. Namm and G. Woo, Introduction to the Theory and Solution Method for Variational Inequalities (Changwon National University Press, Changwon, Korea, 2002).
F. P. Vasil’ev, Numerical Methods for Solving Extremum Problems (Nauka, Moscow, 1980) [in Russian].
R. Glowinski, J.-L. Lions, and R. Tremolieres, Analyse Numérique des Inéquations Variationnelles (Dunod, Paris, 1976; Mir, Moscow, 1979).
R. Glowinski, Numerical Methods for Nonlinear Variational Problems (Springer-Verlag, New York, 1984).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © H. Kim, R.V. Namm, E.M. Vikhtenko, and G. Woo, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 6, pp. 10–19.
About this article
Cite this article
Kim, H., Namm, R.V., Vikhtenko, E.M. et al. Regularization in the Mosolov and Myasnikov problem with boundary friction. Russ Math. 53, 7–14 (2009). https://doi.org/10.3103/S1066369X09060024
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X09060024