Nonlinear Analysis and Control of Physical Processes and Fields

Sinopse

Modern achievements in the intensively developing field of applied mathematicsnbsp;are presented in this monograph. In particular,nbsp;it proposesnbsp;a new approach to extremal problem theory for nonlinear operators, differential-operator equations and inclusions, and for variational inequalities in Banach spaces. An axiomatic study of nonlinear maps (including multi-valued ones) is given, and the properties of resolving operators for systems, consisting of operator and differential-operator equations, are stated in nonlinear-map terms. The solvability conditions and the properties of extremal problem solutions are obtained, whilenbsp;their weak expansions and necessary conditions of optimality in variational inequality form are formulated. In addition. the monograph proposesnbsp;regularization methods and approximation schemes. This book is adressed to scientists, graduates and undergraduates who are interested in nonlinear analysis, control theory, system analysis and differential equations.