Viability, Invariance and Applications
- 1st Edition, Volume 207 - June 4, 2007
- Imprint: Elsevier Science
- Authors: Ovidiu Carja, Mihai Necula, Ioan I. Vrabie
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 4 - 5 5 0 7 8 - 1
- Hardback ISBN:9 7 8 - 0 - 4 4 4 - 5 2 7 6 1 - 5
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 5 2 1 6 6 - 4
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… Read more
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Request a sales quoteThe 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.
- 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
Graduate students, specialists and researchers in O.D.E., P.D.E., Differential Inclusions, Optimal Control. Physicists, Engineers, Chemists, Economists, Biologists
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
- Edition: 1
- Volume: 207
- Published: June 4, 2007
- No. of pages (eBook): 356
- Imprint: Elsevier Science
- Language: English
- Paperback ISBN: 9780444550781
- Hardback ISBN: 9780444527615
- eBook ISBN: 9780080521664
OC
Ovidiu Carja
Affiliations and expertise
Al. I. Cuza University
700506 Iasi, RomaniaMN
Mihai Necula
Affiliations and expertise
Al. I. Cuza University
700506 Iasi, RomaniaIV
Ioan I. Vrabie
Affiliations and expertise
Al. I. Cuza University
700506 Iasi, RomaniaRead Viability, Invariance and Applications on ScienceDirect