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Viability, Invariance and Applications: Volume 207 by Ovidiu Carja, Mihai Necula, Ioan I. Vrabie

Viability, Invariance and Applications: Volume 207

by Ovidiu Carja , Mihai Necula , Ioan I. Vrabie
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Book cover type: Hardcover
  • ISBN13: 9780444527615
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Elsevier Science
  • Publisher Imprint: Elsevier Science
  • Publication Date:
  • Pages: 356
  • Original Price: GBP 85.0
  • Language: English
  • Edition: N/A
  • Item Weight: 781 grams
  • BISAC Subject(s): Differential Equations / Ordinary

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.

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