Singular Nonlinear Partial Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
1996
|
| Schriftenreihe: | Aspects of Mathematics
28 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations. We study the existence of formal power series solutions, holomorphic solutions, and singular solutions of singular non linear partial differential equations. In the first chapter, we introduce operators with regular singularities in the one variable case and we give a new simple proof of the classical Maillet's theorem for algebraic differential equations. In chapter 2, we extend this theory to operators in several variables. The chapter 3 is devoted to the study of formal and convergent power series solutions of a class of singular partial differential equations having a linear part, using the method of iteration and also Newton's method. As an appli cation of the former results, we look in chapter 4 at the local theory of differential equations of the form xy' = 1(x,y) and, in particular, we show how easy it is to find the classical results on such an equation when 1(0,0) = 0 and give also the study of such an equation when 1(0,0) #- 0 which was never given before and can be extended to equations of the form Ty = F(x, y) where T is an arbitrary vector field |
| Beschreibung: | 1 Online-Ressource (VIII, 272 p) |
| ISBN: | 9783322802842 9783322802866 |
| ISSN: | 0179-2156 |
| DOI: | 10.1007/978-3-322-80284-2 |
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| 500 | |a The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations. We study the existence of formal power series solutions, holomorphic solutions, and singular solutions of singular non linear partial differential equations. In the first chapter, we introduce operators with regular singularities in the one variable case and we give a new simple proof of the classical Maillet's theorem for algebraic differential equations. In chapter 2, we extend this theory to operators in several variables. The chapter 3 is devoted to the study of formal and convergent power series solutions of a class of singular partial differential equations having a linear part, using the method of iteration and also Newton's method. As an appli cation of the former results, we look in chapter 4 at the local theory of differential equations of the form xy' = 1(x,y) and, in particular, we show how easy it is to find the classical results on such an equation when 1(0,0) = 0 and give also the study of such an equation when 1(0,0) #- 0 which was never given before and can be extended to equations of the form Ty = F(x, y) where T is an arbitrary vector field | ||
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Datensatz im Suchindex
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| author | Gérard, Raymond |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783322802842 9783322802866 |
| issn | 0179-2156 |
| language | English |
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| spelling | Gérard, Raymond Verfasser aut Singular Nonlinear Partial Differential Equations by Raymond Gérard, Hidetoshi Tahara Wiesbaden Vieweg+Teubner Verlag 1996 1 Online-Ressource (VIII, 272 p) txt rdacontent c rdamedia cr rdacarrier Aspects of Mathematics 28 0179-2156 The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations. We study the existence of formal power series solutions, holomorphic solutions, and singular solutions of singular non linear partial differential equations. In the first chapter, we introduce operators with regular singularities in the one variable case and we give a new simple proof of the classical Maillet's theorem for algebraic differential equations. In chapter 2, we extend this theory to operators in several variables. The chapter 3 is devoted to the study of formal and convergent power series solutions of a class of singular partial differential equations having a linear part, using the method of iteration and also Newton's method. As an appli cation of the former results, we look in chapter 4 at the local theory of differential equations of the form xy' = 1(x,y) and, in particular, we show how easy it is to find the classical results on such an equation when 1(0,0) = 0 and give also the study of such an equation when 1(0,0) #- 0 which was never given before and can be extended to equations of the form Ty = F(x, y) where T is an arbitrary vector field Mathematics Global analysis (Mathematics) Differential equations, partial Partial Differential Equations Analysis Mathematik Singuläre Lösung (DE-588)4290969-7 gnd rswk-swf Singuläre Gleichung (DE-588)4181517-8 gnd rswk-swf Formale Potenzreihe (DE-588)4204495-9 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Holomorphe Lösung (DE-588)4406551-6 gnd rswk-swf Reihenlösung (DE-588)4406554-1 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Formale Potenzreihe (DE-588)4204495-9 s Reihenlösung (DE-588)4406554-1 s 1\p DE-604 Singuläre Lösung (DE-588)4290969-7 s 2\p DE-604 Singuläre Gleichung (DE-588)4181517-8 s 3\p DE-604 Holomorphe Lösung (DE-588)4406551-6 s 4\p DE-604 Tahara, Hidetoshi Sonstige oth https://doi.org/10.1007/978-3-322-80284-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gérard, Raymond Singular Nonlinear Partial Differential Equations Mathematics Global analysis (Mathematics) Differential equations, partial Partial Differential Equations Analysis Mathematik Singuläre Lösung (DE-588)4290969-7 gnd Singuläre Gleichung (DE-588)4181517-8 gnd Formale Potenzreihe (DE-588)4204495-9 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Holomorphe Lösung (DE-588)4406551-6 gnd Reihenlösung (DE-588)4406554-1 gnd |
| subject_GND | (DE-588)4290969-7 (DE-588)4181517-8 (DE-588)4204495-9 (DE-588)4128900-6 (DE-588)4406551-6 (DE-588)4406554-1 |
| title | Singular Nonlinear Partial Differential Equations |
| title_auth | Singular Nonlinear Partial Differential Equations |
| title_exact_search | Singular Nonlinear Partial Differential Equations |
| title_full | Singular Nonlinear Partial Differential Equations by Raymond Gérard, Hidetoshi Tahara |
| title_fullStr | Singular Nonlinear Partial Differential Equations by Raymond Gérard, Hidetoshi Tahara |
| title_full_unstemmed | Singular Nonlinear Partial Differential Equations by Raymond Gérard, Hidetoshi Tahara |
| title_short | Singular Nonlinear Partial Differential Equations |
| title_sort | singular nonlinear partial differential equations |
| topic | Mathematics Global analysis (Mathematics) Differential equations, partial Partial Differential Equations Analysis Mathematik Singuläre Lösung (DE-588)4290969-7 gnd Singuläre Gleichung (DE-588)4181517-8 gnd Formale Potenzreihe (DE-588)4204495-9 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Holomorphe Lösung (DE-588)4406551-6 gnd Reihenlösung (DE-588)4406554-1 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Differential equations, partial Partial Differential Equations Analysis Mathematik Singuläre Lösung Singuläre Gleichung Formale Potenzreihe Nichtlineare partielle Differentialgleichung Holomorphe Lösung Reihenlösung |
| url | https://doi.org/10.1007/978-3-322-80284-2 |
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