Viability, Invariance and Applications : Volume 207 Hardback
Part of the North-Holland Mathematics Studies series
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.
- Format: Hardback
- Pages: 356 pages
- Publisher: Elsevier Science & Technology
- Publication Date: 04/06/2007
- Category: Differential calculus & equations
- ISBN: 9780444527615