Viability, Invariance and Applications
( Volume 207 )
Publication series ：Volume 207
Author： Carja Ovidiu;Necula Mihai;Vrabie Ioan I.
Publisher： Elsevier Science
Publication year： 2007
E-ISBN: 9780080521664
P-ISBN(Paperback): 9780444527615
P-ISBN(Hardback): 9780444527615
Subject： O1 Mathematics;O175 differential equations, integral equations;O241 数值分析
Language： ENG
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Description
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 inc
Chapter