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: | FAW01 FAW02 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 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 Includes bibliographical references (p. 325-333) and indexes |
| Beschreibung: | 1 Online-Ressource (xii, 344 p.) |
| ISBN: | 0080521665 0444527613 9780080521664 9780444527615 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043044055 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 151123s2007 |||| o||u| ||||||eng d | ||
| 020 | |a 0080521665 |c electronic bk. |9 0-08-052166-5 | ||
| 020 | |a 0444527613 |9 0-444-52761-3 | ||
| 020 | |a 9780080521664 |c electronic bk. |9 978-0-08-052166-4 | ||
| 020 | |a 9780444527615 |9 978-0-444-52761-5 | ||
| 035 | |a (OCoLC)162131435 | ||
| 035 | |a (DE-599)BVBBV043044055 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-1047 | ||
| 082 | 0 | |a 515.35 |2 22 | |
| 100 | 1 | |a Cârjă, Ovidiu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Viability, invariance and applications |c Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie |
| 250 | |a 1st ed | ||
| 264 | 1 | |a Amsterdam |b Elsevier |c 2007 | |
| 300 | |a 1 Online-Ressource (xii, 344 p.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 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 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 | ||
| 500 | |a Includes bibliographical references (p. 325-333) and indexes | ||
| 650 | 7 | |a MATHEMATICS / Differential Equations / General |2 bisacsh | |
| 650 | 7 | |a Differential equations |2 fast | |
| 650 | 7 | |a Set theory |2 fast | |
| 650 | 7 | |a Symmetry (Mathematics) |2 fast | |
| 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 | |
| 856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196523 |x Aggregator |3 Volltext |
| 912 | |a ZDB-4-EBA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028468592 | ||
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196523 |l FAW01 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196523 |l FAW02 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804175409453989888 |
|---|---|
| any_adam_object | |
| author | Cârjă, Ovidiu |
| author_facet | Cârjă, Ovidiu |
| author_role | aut |
| author_sort | Cârjă, Ovidiu |
| author_variant | o c oc |
| building | Verbundindex |
| bvnumber | BV043044055 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)162131435 (DE-599)BVBBV043044055 |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04566nmm a2200517zcb4500</leader><controlfield tag="001">BV043044055</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151123s2007 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0080521665</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">0-08-052166-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0444527613</subfield><subfield code="9">0-444-52761-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780080521664</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-0-08-052166-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780444527615</subfield><subfield code="9">978-0-444-52761-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)162131435</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043044055</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-1047</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.35</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cârjă, Ovidiu</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Viability, invariance and applications</subfield><subfield code="c">Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1st ed</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Amsterdam</subfield><subfield code="b">Elsevier</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xii, 344 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">North-Holland mathematics studies</subfield><subfield code="v">207</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (p. 325-333) and indexes</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Differential Equations / General</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Differential equations</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Set theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Symmetry (Mathematics)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Set theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symmetry (Mathematics)</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Necula, Mihai</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Vrabie, I. I.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196523</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028468592</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196523</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196523</subfield><subfield code="l">FAW02</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043044055 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:50Z |
| institution | BVB |
| isbn | 0080521665 0444527613 9780080521664 9780444527615 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028468592 |
| oclc_num | 162131435 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xii, 344 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Elsevier |
| record_format | marc |
| 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 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 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://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196523 Aggregator 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://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196523 |
| work_keys_str_mv | AT carjaovidiu viabilityinvarianceandapplications AT neculamihai viabilityinvarianceandapplications AT vrabieii viabilityinvarianceandapplications |