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S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Master's Degree_수리과학부)

Remarks on the existence theories of ordinary differential equations : 상미분 방정식의 존재성 이론에 관한 언급

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dc.contributor.advisor하승열-
dc.contributor.authorSokun Kim-
dc.date.accessioned2017-07-19T09:01:29Z-
dc.date.available2017-07-19T09:01:29Z-
dc.date.issued2016-08-
dc.identifier.other000000136299-
dc.identifier.urihttps://hdl.handle.net/10371/131510-
dc.description학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 하승열.-
dc.description.abstractIn this thesis, we review the state-of-art in the existence theories of ordinary differential equations. More precisely, we discuss the Cauchy-Lipschitz theory, Carathéodory theory, Picard-Lindelöf theory, Peano theory and Osgood conditions for the classical solution. For discontinuous forcing, we introduce Filippov theory and generalized theory by Luigi Ambrosio, Camillo De Lellis and Gianluca Crippa.-
dc.description.tableofcontentsChapter 1 Introduction 1
1.1 First-order equations 1
1.2 Initial-value problem 4
1.3 First-order system of ordinary differential equations 5

Chapter 2 Cauchy-Lipschitz theorem 7
2.1 Lipschitz condition 7
2.2 The existence and uniqueness theorem 8

Chapter 3 Carathéodory theorem 17
3.1 The main definition 17
3.2 Carathéodorys condition 18
3.3 The existence and uniqueness theorem 18

Chapter 4 Osgood criterion 22
4.1 Osgoods uniqueness theorem 22

Chapter 5 Generalized theorem 26
5.1 The main definition 26
5.2 Classical setting of existence and uniqueness 27
5.3 Classical flow of a vector field 33
5.4 Transport and continuity equation 36

Chapter 6 Summary and Conclusion 39

Bibliography 40

국문 초록 42		-
dc.formatapplication/pdf-
dc.format.extent2784022 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subjectOrdinary differential equations-
dc.subjectexistence-
dc.subjectuniqueness-
dc.subjectLipschitz condition-
dc.subjectCarathéodory theorem-
dc.subjectOsgood criterion-
dc.subjectPicard-Lindelöf theorem-
dc.subjectPeano theorem-
dc.subjectgeneralized theorem-
dc.subject.ddc510-
dc.titleRemarks on the existence theories of ordinary differential equations-
dc.title.alternative상미분 방정식의 존재성 이론에 관한 언급-
dc.typeThesis-
dc.contributor.AlternativeAuthor김소쿤-
dc.description.degreeMaster-
dc.citation.pages49-
dc.contributor.affiliation자연과학대학 수리과학부-
dc.date.awarded2016-08-
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Master's Degree_수리과학부)
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