On Some Recent Developments Concerning Moreau’s Sweeping Process

The main objective of this paper is to present an overview of Moreau’s sweeping process —u’(t) ∈ N c (t) (u (t)) along with some of our results concerning new variants of this process. Several open problems are mentioned.

[1]  Leonid Prigozhin,et al.  Variational model of sandpile growth , 1996, European Journal of Applied Mathematics.

[2]  H. Benabdellah.  Existence of Solutions to the Nonconvex Sweeping Process , 2000 .

[3]  Markus Kunze,et al.  Degenerate Sweeping Processes , 1999 .

[4]  M. Marques,et al.  Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction , 1993 .

[5]  Wolfgang Desch.  Local Lipschitz continuity of the stop operator , 1998 .

[6]  R. Glowinski,et al.  Numerical Analysis of Variational Inequalities , 1981 .

[7]  J. Moreau.  Numerical aspects of the sweeping process , 1999 .

[8]  P. Argoul,et al.  IUTAM Symposium on Variations of domains and free-boundary problems in solid mechanics , 1999 .

[9]  Weimin Han,et al.  Qualitative and Numerical Analysis of Quasi-Static Problems in Elastoplasticity , 1997 .

[10]  A. H. Siddiqi,et al.  CERTAIN REMARKS ON A CLASS OF EVOLUTION QUASI-VARIATIONAL INEQUALITIES , 2000 .

[11]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[12]  G. Colombo,et al.  The Sweeping Processes without Convexity , 1999 .

[13]  Pavel Krejčí,et al.  Hysteresis, convexity and dissipation in hyperbolic equations , 1996 .

[14]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[15]  Charles Castaing,et al.  Periodic solutions of evolution problem associated with moving convex sets , 1995 .

[16]  Paul Germain,et al.  Applications of methods of functional analysis to problems in mechanics : Joint symposium IUTAM/IMU held in Marseille, September 1-6, 1975 , 1976 .

[17]  A. Sändig,et al.  Nonlinear Differential Equations , 1980 .

[18]  M. Marques,et al.  BV periodic solutions of an evolution problem associated with continuous moving convex sets , 1995 .

[19]  Manuel D. P. Monteiro Marques,et al.  Regularization and graph approximation of a discontinuous evolution problem , 1987 .

[20]  Charles Castaing,et al.  Topological properties of solution sets for sweeping processes with delay. , 1997 .

[21]  Markus Kunze,et al.  On parabolic quasi-variational inequalities and state-dependent sweeping processes , 1998 .

[22]  J. Moreau.  Evolution problem associated with a moving convex set in a Hilbert space , 1977 .

[23]  C. Baiocchi,et al.  Variational and quasivariational inequalities: Applications to free boundary problems , 1983 .

[24]  Markus Kunze,et al.  An Introduction to Moreau’s Sweeping Process , 2000 .

[25]  Leonid Prigozhin,et al.  On the Bean critical-state model in superconductivity , 1996, European Journal of Applied Mathematics.

[26]  Alain Bensoussan,et al.  Impulse Control and Quasi-Variational Inequalities , 1984 .

[27]  J. S. Raymond.  A generalization of Lax-Milgram's theorem , 1998 .

[28]  J. Moreau.  Application of convex analysis to the treatment of elastoplastic systems , 1976 .

[29]  M. Kunze,et al.  Existence of Solutions for Degenerate Sweeping Processes , 1997 .

[30]  M. Kunze.  Periodic solutions of non-linear kinematic hardening models , 1999 .

[31]  José Francisco Rodrigues,et al.  An elliptic quasi-variational inequality with gradient constraints and some of its applications , 2000 .

[32]  M. Marques.  Differential Inclusions in Nonsmooth Mechanical Problems , 1993 .