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

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


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About the Book

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.

Table of Contents:
1. Generalities2. Specific preliminary results Ordinary differential equations and inclusions3. Nagumo type viability theorems4. Problems of invariance5. Viability under Carathéodory conditions6. Viability for differential inclusions7. Applications Part 2 Evolution equations and inclusions8. Viability for single-valued semilinear evolutions 9. Viability for multi-valued semilinear evolutions10. Viability for single-valued fully nonlinear evolutions11. Viability for multi-valued fully nonlinear evolutions12. Carathéodory perturbations of m-dissipative operators13. Applications

Review :
"This book deals with a systematic treatment of those tangency conditions in connection with viability or invariance problems of increasing generality, together with some applications of the previously developed abstract theory. The material is presented in a very clear and well-organized way." --Zentralblatt MATH, 2012


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Product Details
  • ISBN-13: 9780444527615
  • Publisher: Elsevier Science & Technology
  • Publisher Imprint: Elsevier Science Ltd
  • Height: 240 mm
  • No of Pages: 356
  • Sub Title: Volume 207
  • Width: 165 mm
  • ISBN-10: 0444527613
  • Publisher Date: 04 Jun 2007
  • Binding: Hardback
  • Language: English
  • Series Title: Volume 207 North-Holland Mathematics Studies
  • Weight: 730 gr


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