Viability, invariance and applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2007
|
| Ausgabe: | 1st ed |
| Schriftenreihe: | North-Holland mathematics studies
207 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 Includes bibliographical references (p. 325-333) and indexes |
| Beschreibung: | 1 Online-Ressource (xii, 344 p.) |
| ISBN: | 9780444527615 0444527613 9780080521664 0080521665 |
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| 245 | 1 | 0 | |a Viability, invariance and applications |c Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie |
| 250 | |a 1st ed | ||
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| 490 | 0 | |a North-Holland mathematics studies |v 207 | |
| 500 | |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 | ||
| 500 | |a Includes bibliographical references (p. 325-333) and indexes | ||
| 650 | 7 | |a MATHEMATICS / Differential Equations / General |2 bisacsh | |
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| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Set theory | |
| 650 | 4 | |a Symmetry (Mathematics) | |
| 700 | 1 | |a Necula, Mihai |e Sonstige |4 oth | |
| 700 | 1 | |a Vrabie, I. I. |e Sonstige |4 oth | |
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Datensatz im Suchindex
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| author | Cârjă, Ovidiu |
| author_facet | Cârjă, Ovidiu |
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| author_sort | Cârjă, Ovidiu |
| author_variant | o c oc |
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| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
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| id | DE-604.BV042317168 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:16Z |
| institution | BVB |
| isbn | 9780444527615 0444527613 9780080521664 0080521665 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027754159 |
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| physical | 1 Online-Ressource (xii, 344 p.) |
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| publishDate | 2007 |
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| publisher | Elsevier |
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| series2 | North-Holland mathematics studies |
| spelling | Cârjă, Ovidiu Verfasser aut Viability, invariance and applications Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie 1st ed Amsterdam Elsevier 2007 1 Online-Ressource (xii, 344 p.) txt rdacontent c rdamedia cr rdacarrier North-Holland mathematics studies 207 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 Includes bibliographical references (p. 325-333) and indexes MATHEMATICS / Differential Equations / General bisacsh Differential equations fast Set theory fast Symmetry (Mathematics) fast Differential equations Set theory Symmetry (Mathematics) Necula, Mihai Sonstige oth Vrabie, I. I. Sonstige oth http://www.sciencedirect.com/science/book/9780444527615 Verlag Volltext |
| spellingShingle | Cârjă, Ovidiu Viability, invariance and applications MATHEMATICS / Differential Equations / General bisacsh Differential equations fast Set theory fast Symmetry (Mathematics) fast Differential equations Set theory Symmetry (Mathematics) |
| title | Viability, invariance and applications |
| title_auth | Viability, invariance and applications |
| title_exact_search | Viability, invariance and applications |
| title_full | Viability, invariance and applications Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie |
| title_fullStr | Viability, invariance and applications Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie |
| title_full_unstemmed | Viability, invariance and applications Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie |
| title_short | Viability, invariance and applications |
| title_sort | viability invariance and applications |
| topic | MATHEMATICS / Differential Equations / General bisacsh Differential equations fast Set theory fast Symmetry (Mathematics) fast Differential equations Set theory Symmetry (Mathematics) |
| topic_facet | MATHEMATICS / Differential Equations / General Differential equations Set theory Symmetry (Mathematics) |
| url | http://www.sciencedirect.com/science/book/9780444527615 |
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