Viability, Invariance and Applications (North-Holland Mathematics Studies, Volume 207) - ISBN:0444527613

Viability, Invariance and Applications (North-Holland Mathematics Studies, Volume 207)

Date: 14 April 2011, 03:43

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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.
[list][*] 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

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