The idea for this book was developed in the seminar on problems of conยญ tinuum mechanics, which has been active for more than twelve years at the Faculty of Mathematics and Physics, Charles University, Prague. This seminar has been pursuing recent directions in the development of matheยญ matical applications in physics; especially in continuum mechanics, and in technology. It has regularly been attended by upper division and graduate students, faculty, and scientists and researchers from various institutions from Prague and elsewhere. These seminar participants decided to publish in a self-contained monograph the results of their individual and collective efforts in developing applications for the theory of variational inequalities, which is currently a rapidly growing branch of modern analysis. The theory of variational inequalities is a relatively young mathematical discipline. Apparently, one of the main bases for its development was the paper by G. Fichera (1964) on the solution of the Signorini problem in the theory of elasticity. Later, J. L. Lions and G. Stampacchia (1967) laid the foundations of the theory itself. Time-dependent inequalities have primarily been treated in works of J. L. Lions and H. Bnlzis. The diverse applications of the variational inยญ equalities theory are the topics of the well-known monograph by G. Duยญ vaut and J. L. Lions, Les iniquations en micanique et en physique (1972)
CONTENT
Contents: Unilateral Problems for Scalar Functions: Unilateral Boundary Value Problems for Second Order Equations. Problems with Inner Obstacles for Second-Order Operators -- One-Sided Contact of Elastic Bodies: Formulations of Contact Problems. Existence and Uniqueness of Solution. Solution of Primal Problems by the Finite Element Method. Dual Variational Formulation of the Problem with Bounded Zone of Contact. Contact Problems with Friction -- Problems of the Theory of Plasticity: Prandtl-Reuss Model of Plastic Flow. Plastic Flow with Isotropic or Kinematic Hardening -- References -- Index
Physics
Physics
Theoretical Mathematical and Computational Physics
