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...

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Cârjă, Ovidiu
Weitere Verfasser:	Necula, Mihai, Vrabie, I. I. (Ioan I.), 1951-
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Amsterdam ; Boston : Elsevier, 2007.
Ausgabe:	1st ed.
Schriftenreihe:	North-Holland mathematics studies ; 207.
Schlagworte:	Differential equations. Set theory. Symmetry (Mathematics) Équations différentielles. Théorie des ensembles. Symétrie (Mathématiques) MATHEMATICS > Differential Equations > General. Differential equations Set theory dissertations. Academic theses Academic theses. Thèses et écrits académiques.
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Zusammenfassung:	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 Nagumos 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.
Beschreibung:	1 online resource (xii, 344 pages) : illustrations
Bibliographie:	Includes bibliographical references (pages 325-333) and indexes.
ISBN:	9780444527615 0444527613 9780080521664 0080521665 1281021555 9781281021557
ISSN:	0304-0208 ;