| Description |
1 online resource (xii, 344 pages) : illustrations |
| Series |
North-Holland mathematics studies, 0304-0208 ; 207 |
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North-Holland mathematics studies ; 207. 0304-0208
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| Contents |
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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 325-333) and indexes |
| Notes |
Print version record |
| Subject |
Differential equations.
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Set theory.
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Symmetry (Mathematics)
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MATHEMATICS -- Differential Equations -- General.
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Differential equations
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Set theory
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Symmetry (Mathematics)
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| Genre/Form |
dissertations.
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Academic theses
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Academic theses.
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Thèses et écrits académiques.
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| Form |
Electronic book
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| Author |
Necula, Mihai.
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Vrabie, I. I. (Ioan I.), 1951-
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| ISBN |
9780444527615 |
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0444527613 |
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9780080521664 |
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0080521665 |
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1281021555 |
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9781281021557 |
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