viability invariance and applications

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Viability, Invariance and Applications
Author : Ovidiu Carja,Mihai Necula,Ioan I. Vrabie
Publisher : Elsevier
Release Date : 2007-07-18
ISBN 10 : 9780080521664
Pages : 356 pages
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The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time. The book includes the most important necessary and sufficient conditions for viability starting with Nagumo’s Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. New concepts for multi-functions as the classical tangent vectors for functions Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions Clarifying examples, illustrations and numerous problems, completely and carefully solved Illustrates the applications from theory into practice Very clear and elegant style

Viability Theory
Author : Jean-Pierre Aubin,Alexandre M. Bayen,Patrick Saint-Pierre
Publisher : Springer Science & Business Media
Release Date : 2011-07-13
ISBN 10 : 9783642166846
Pages : 803 pages
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Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and illustrating them with numerous numerical examples taken from various fields.

Analele Științifice Ale Universității
Author : N.A
Publisher : N.A
Release Date : 2008
ISBN 10 :
Pages : 329 pages
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Value Functions in Control Systems and Differential Games
Author : Sławomir Plaskacz
Publisher : N.A
Release Date : 2003
ISBN 10 :
Pages : 119 pages
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Differential Equations
Author : Ioan I Vrabie
Publisher : World Scientific Publishing Company
Release Date : 2016-05-30
ISBN 10 : 981474980X
Pages : 528 pages
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This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, and gradient systems. In this new edition, some typos have been corrected and two new topics have been added: Delay differential equations and differential equations subjected to nonlocal initial conditions. The bibliography has also been updated and expanded.

Differential Equations
Author : Ioan I. Vrabie
Publisher : World Scientific
Release Date : 2004
ISBN 10 : 9789812388384
Pages : 401 pages
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This book presents the main concepts and results of differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, gradient systems.

Mathematical Analysis and Applications
Author : V. Rădulescu,Vicentiu D. Radulescu,Constantin Niculescu (P.)
Publisher : American Institute of Physics
Release Date : 2006-05-25
ISBN 10 :
Pages : 167 pages
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This book comprises the proceedings of the International Conference on Mathematical Analysis and Applications, held in Craiova, Romania, 23-24 September 2005. The peer-reviewed papers presented here cover a range of topics at the interface between mathematical physics, numerical analysis, optimal control, and calculus of variations. The coverage includes nonlinear analysis and partial differential equations as well as classical mathematical analysis and dynamical systems.

Dynamic Systems and Applications
Author : N.A
Publisher : N.A
Release Date : 2003
ISBN 10 :
Pages : 329 pages
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Co-Semigroups and Applications
Author : Ioan I. Vrabie
Publisher : Elsevier
Release Date : 2003-03-21
ISBN 10 : 9780080530048
Pages : 396 pages
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The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of Co-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigroups such as equicontinuous, compact, differentiable, or analytic, as well as to some nonstandard types of partial differential equations, i.e. elliptic and parabolic systems with dynamic boundary conditions, and linear or semilinear differential equations with distributed (time, spatial) measures. Moreover, some finite-dimensional-like methods for certain semilinear pseudo-parabolic, or hyperbolic equations are also disscussed. Among the most interesting applications covered are not only the standard ones concerning the Laplace equation subject to either Dirichlet, or Neumann boundary conditions, or the Wave, or Klein-Gordon equations, but also those referring to the Maxwell equations, the equations of Linear Thermoelasticity, the equations of Linear Viscoelasticity, to list only a few. Moreover, each chapter contains a set of various problems, all of them completely solved and explained in a special section at the end of the book. The book is primarily addressed to graduate students and researchers in the field, but it would be of interest for both physicists and engineers. It should be emphasised that it is almost self-contained, requiring only a basic course in Functional Analysis and Partial Differential Equations.

SIAM Journal on Control and Optimization
Author : Society for Industrial and Applied Mathematics
Publisher : N.A
Release Date : 2002
ISBN 10 :
Pages : 329 pages
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Nonlinear Partial Differential Equations with Applications
Author : Tomás Roubicek
Publisher : Springer Science & Business Media
Release Date : 2005-09-16
ISBN 10 : 9783764372934
Pages : 405 pages
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This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

Journal of analysis and its application
Author : N.A
Publisher : N.A
Release Date : 2004
ISBN 10 :
Pages : 329 pages
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