Viability, Invariance and Applications: Volume 207

By Mihai Necula, Ovidiu Carja, Ioan I. Vrabie

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: Hardcover
• Language: English
• ISBN: 0444527613
• ISBN13: 9780444527615
• Release Date: August 2007
• Publisher: Elsevier Science
• Length: 356 Pages
• Weight: 1.72 lbs.
• Dimensions: 0.8" x 6.8" x 9.5"