| Edition |
1st ed. |
| Description |
1 online resource (xii, 344 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
North-Holland mathematics studies, 0304-0208 ; 207 |
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North-Holland mathematics studies ; 207. 0304-0208
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| 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. |
| 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 Caratodory 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. Caratodory perturbations of m-dissipative operators -- Chapter 13. Applications -- Solutions to the proposed problems -- Bibliographical notes and comments -- Bibliography -- Name Index -- Subject Index -- Notation. |
| Bibliography |
Includes bibliographical references (pages 325-333) and indexes. |
| Note |
Print version record. |
| Subject |
Differential equations.
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Set theory.
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Symmetry (Mathematics)
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Équations différentielles.
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Théorie des ensembles.
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Symétrie (Mathématiques)
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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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| Added Author |
Necula, Mihai.
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Vrabie, I. I. (Ioan I.), 1951-
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| Other Form: |
Print version: Cârj, Ovidiu. Viability, invariance and applications. 1st ed. Amsterdam ; Boston : Elsevier, 2007 9780444527615 0444527613 (OCoLC)85690133 |
| ISBN |
9780444527615 |
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0444527613 |
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9780080521664 (electronic bk.) |
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0080521665 (electronic bk.) |
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1281021555 |
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9781281021557 |
| Standard No. |
AU@ 000048130579 |
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AU@ 000051560101 |
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AU@ 000059268287 |
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CHNEW 001006047 |
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DEBBG BV036962185 |
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DEBBG BV039834066 |
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DEBBG BV042317168 |
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DEBBG BV043044055 |
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DEBSZ 276312066 |
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DEBSZ 422198277 |
|
DEBSZ 482354062 |
|
NZ1 11778298 |
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NZ1 14540172 |
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NZ1 15177282 |
|
