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Viability, invariance and applications /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; Boston :
Elsevier,
2007.
|
| Edición: | 1st ed. |
| Colección: | North-Holland mathematics studies ;
207. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Cârjă, Ovidiu. | |
| 245 | 1 | 0 | |a Viability, invariance and applications / |c Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie. |
| 250 | |a 1st ed. | ||
| 260 | |a Amsterdam ; |a Boston : |b Elsevier, |c 2007. | ||
| 300 | |a 1 online resource (xii, 344 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a North-Holland mathematics studies, |x 0304-0208 ; |v 207 | |
| 520 | |a 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 Nagumos 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. | ||
| 505 | 0 | |a Preface -- Chapter 1. Generalities -- Chapter 2. Specific preliminary results -- Ordinary differential equations and inclusions -- Chapter 3. Nagumo type viability theorems -- Chapter 4. Problems of invariance -- Chapter 5. Viability under Caratȟodory conditions -- Chapter 6. Viability for differential inclusions -- Chapter 7. Applications -- Part 2 Evolution equations and inclusions -- Chapter 8. Viability for single-valued semilinear evolutions -- Chapter 9. Viability for multi-valued semilinear evolutions -- Chapter 10. Viability for single-valued fully nonlinear evolutions -- Chapter 11. Viability for multi-valued fully nonlinear evolutions -- Chapter 12. Caratȟodory perturbations of m-dissipative operators -- Chapter 13. Applications -- Solutions to the proposed problems -- Bibliographical notes and comments -- Bibliography -- Name Index -- Subject Index -- Notation. | |
| 504 | |a Includes bibliographical references (pages 325-333) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Set theory. | |
| 650 | 0 | |a Symmetry (Mathematics) | |
| 650 | 6 | |a Équations différentielles. | |
| 650 | 6 | |a Théorie des ensembles. | |
| 650 | 6 | |a Symétrie (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Differential equations |2 fast | |
| 650 | 7 | |a Set theory |2 fast | |
| 650 | 7 | |a Symmetry (Mathematics) |2 fast | |
| 700 | 1 | |a Necula, Mihai. | |
| 700 | 1 | |a Vrabie, I. I. |q (Ioan I.), |d 1951- | |
| 776 | 0 | 8 | |i Print version: |a Cârjă, Ovidiu. |t Viability, invariance and applications. |b 1st ed. |d Amsterdam ; Boston : Elsevier, 2007 |z 9780444527615 |z 0444527613 |w (OCoLC)85690133 |
| 830 | 0 | |a North-Holland mathematics studies ; |v 207. |x 0304-0208 | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=196523 |z Texto completo |
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