Springer Variational and Quasi-Variational Inequalities in Mechanics: 147 (Solid Mechanics and Its Applications, 147)

The essential aim of this book is to consider a wide set of problems arising in the mathematical modeling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities and their transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems. Review From the reviews: "The main idea of the presented monograph is to deal with mathematical models connected with mechanical systems under unilateral constraints. … Examples of analytical and numerical solutions are presented. Numerical solutions were obtained using the finite element and boundary element methods. … The text contains a big amount of latest results achieved in mathematical modeling of contact problems in mechanics together with applications. It can be recommended both to graduate students and the researchers in applied mathematics and mechanics." (Igor Bock, Zentralblatt MATH, Vol. 1131 (9), 2008) "The aim of this interesting book is the study of problems in the mathematical modelling of mechanical systems … . The work is intended for a wide audience: this would include specialists in contact processes in structural and mechanical systems … as well as those with a background in the mathematical sciences who seek a self-contained account of the mathematical theory of contact mechanics. The text is suitable for graduate students and researchers in applied mathematics, computational mathematics, and computational mechanics." (Ján Lovišek, Mathematical Reviews, Issue 2009 e)