다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Stochastic equations in infinite dimensions

“Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.

SET-Valued Analysis

Rate-independent systems occur as limit problems in many physical and mechanical problems, if the interesting time scales are much longer than the intrinsic time scales in the system. Rate-independent systems are sometimes also called “quasistatic systems,” however, the term “quasistatic” is often used in a more general sense—namely, if the inertial terms in a system are neglected, but viscous effects might still be present. The chapter discusses different aspects of rate-independent models or hysteresis operators in the context of continuum mechanics. There are several areas in these fields that have evolved quite independently and have developed their own languages and notation. The chapter compares these different approaches by translating them into one language, and thus provides a useful overview of the different methods in the field.

Chapter 6 - Evolution of Rate-Independent Systems

This text provides a complete introduction to the theory of variational inequalities with emphasis on contact mechanics. It covers existence, uniqueness and convergence results for variational inequalities, including the modelling and variational analysis of specific frictional contact problems with elastic, viscoelastic and viscoplastic materials. New models of contact are presented, including contact of piezoelectric materials. Particular attention is paid to the study of history-dependent quasivariational inequalities and to their applications in the study of contact problems with unilateral constraints. The book fully illustrates the cross-fertilisation between modelling and applications on the one hand and nonlinear mathematical analysis on the other. Indeed, the reader will gain an understanding of how new and nonstandard models in contact mechanics lead to new types of variational inequalities and, conversely, how abstract results concerning variational inequalities can be applied to prove the unique solvability of the corresponding contact problems.

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Mathematical Models in Contact Mechanics

Numerical analysis and simulations of a dynamic frictionless contact problem with damage

We develop the theory of evolution inclusions for set-valued pseudomonotone maps. The problems we investigate are where B=B(t) is a linear operator that may vanish and A is a set-valued pseudomonotone operator. We prove the existence of unique solutions of such, possibly degenerate, problems. We apply the theory to the problem of dynamic frictional contact with a slip dependent friction coefficient and prove the existence of its unique weak solution. This theory opens the way for the investigation of sophisticated dynamical models in mechanics and frictional contact problems.

Kenneth L. Kuttler

Papers

Numerical analysis and simulations of a dynamic frictionless contact problem with damage

Set-valued pseudomonotone maps and degenerate evolution inclusions

Second Order Evolution Equations With Dynamic Boundary Conditions

Dynamic friction contact problems for general normal and friction laws

Existence and Uniqueness of Solutions for a Dynamic One-Dimensional Damage Model