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Modern achievements in the intensively developing field of applied
mathematics are presented in this monograph. In particular, it
proposes 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, while their weak
expansions and necessary conditions of optimality in variational
inequality form are formulated. In addition. the monograph proposes
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.
Here, the authors present modern mathematical methods to solve
problems of differential-operator inclusions and evolution
variation inequalities which may occur in fields such as
geophysics, aerohydrodynamics, or fluid dynamics. For the first
time, they describe the detailed generalization of various
approaches to the analysis of fundamentally nonlinear models and
provide a toolbox of mathematical equations. These new mathematical
methods can be applied to a broad spectrum of problems. Examples of
these are phase changes, diffusion of electromagnetic, acoustic,
vibro-, hydro- and seismoacoustic waves, or quantum mechanical
effects. This is the second of two volumes dealing with the
subject.
Modern achievements in the intensively developing field of applied mathematics as applied to physical chemistry are presented in this monograph. In particular, it proposes 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, while their weak expansions and necessary conditions of optimality in variational inequality form are formulated. In addition. the monograph proposes 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.
Here, the authors present modern mathematical methods to solve
problems of differential-operator inclusions and evolution
variation inequalities which may occur in fields such as
geophysics, aerohydrodynamics, or fluid dynamics. For the first
time, they describe the detailed generalization of various
approaches to the analysis of fundamentally nonlinear models and
provide a toolbox of mathematical equations. These new mathematical
methods can be applied to a broad spectrum of problems. Examples of
these are phase changes, diffusion of electromagnetic, acoustic,
vibro-, hydro- and seismoacoustic waves, or quantum mechanical
effects. This is the first of two volumes dealing with the subject.
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