Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1989
|
| Schriftenreihe: | Progress in Nonlinear Differential Equations and Their Applications
130 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and commutators in the study of solutions to nonlinear wave equations. The weak singularities in the solutions to such equations behave up to a certain extent like those present in the linear case: they propagate along the null bicharacteristics of the operator. On the other hand. examples exhibiting singularities not present in the linear case can also be constructed. I have tried to present a crossection of both the regularity results and the singular examples. for problems on the interior of a domain and on domains with boundary. The main emphasis is on the case of more than one space dimen sion. since that case is treated in great detail in the paper of Rauch-Reed 159]. The results presented here have for the most part appeared elsewhere. and are the work of many authors. but a few new examples and proofs are given. I have attempted to indicate the essential ideas behind the arguments. so that only some of the results are proved in full detail. It is hoped that the central notions of the more technical proofs appearing in research papers will be illuminated by these simpler cases |
| Beschreibung: | 1 Online-Ressource (IX, 145 p) |
| ISBN: | 9781461245544 9780817634490 |
| DOI: | 10.1007/978-1-4612-4554-4 |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Beals, Michael |
| author_facet | Beals, Michael |
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| author_sort | Beals, Michael |
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| building | Verbundindex |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4554-4 |
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| id | DE-604.BV042420311 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461245544 9780817634490 |
| language | English |
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| series2 | Progress in Nonlinear Differential Equations and Their Applications |
| spelling | Beals, Michael Verfasser aut Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems by Michael Beals Boston, MA Birkhäuser Boston 1989 1 Online-Ressource (IX, 145 p) txt rdacontent c rdamedia cr rdacarrier Progress in Nonlinear Differential Equations and Their Applications 130 This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and commutators in the study of solutions to nonlinear wave equations. The weak singularities in the solutions to such equations behave up to a certain extent like those present in the linear case: they propagate along the null bicharacteristics of the operator. On the other hand. examples exhibiting singularities not present in the linear case can also be constructed. I have tried to present a crossection of both the regularity results and the singular examples. for problems on the interior of a domain and on domains with boundary. The main emphasis is on the case of more than one space dimen sion. since that case is treated in great detail in the paper of Rauch-Reed 159]. The results presented here have for the most part appeared elsewhere. and are the work of many authors. but a few new examples and proofs are given. I have attempted to indicate the essential ideas behind the arguments. so that only some of the results are proved in full detail. It is hoped that the central notions of the more technical proofs appearing in research papers will be illuminated by these simpler cases Mathematics Differential equations, partial Partial Differential Equations Mathematik Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Nichtlineare Wellengleichung (DE-588)4042104-1 gnd rswk-swf Mikrolokale Analysis (DE-588)4169832-0 gnd rswk-swf Nichtlineare Wellengleichung (DE-588)4042104-1 s Mikrolokale Analysis (DE-588)4169832-0 s 1\p DE-604 Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 s Singularität Mathematik (DE-588)4077459-4 s 2\p DE-604 Wellengleichung (DE-588)4065315-8 s Numerisches Verfahren (DE-588)4128130-5 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-4554-4 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 |
| spellingShingle | Beals, Michael Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems Mathematics Differential equations, partial Partial Differential Equations Mathematik Numerisches Verfahren (DE-588)4128130-5 gnd Wellengleichung (DE-588)4065315-8 gnd Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd Singularität Mathematik (DE-588)4077459-4 gnd Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4065315-8 (DE-588)4228136-2 (DE-588)4077459-4 (DE-588)4042104-1 (DE-588)4169832-0 |
| title | Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems |
| title_auth | Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems |
| title_exact_search | Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems |
| title_full | Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems by Michael Beals |
| title_fullStr | Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems by Michael Beals |
| title_full_unstemmed | Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems by Michael Beals |
| title_short | Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems |
| title_sort | propagation and interaction of singularities in nonlinear hyperbolic problems |
| topic | Mathematics Differential equations, partial Partial Differential Equations Mathematik Numerisches Verfahren (DE-588)4128130-5 gnd Wellengleichung (DE-588)4065315-8 gnd Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd Singularität Mathematik (DE-588)4077459-4 gnd Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd |
| topic_facet | Mathematics Differential equations, partial Partial Differential Equations Mathematik Numerisches Verfahren Wellengleichung Nichtlineare hyperbolische Differentialgleichung Singularität Mathematik Nichtlineare Wellengleichung Mikrolokale Analysis |
| url | https://doi.org/10.1007/978-1-4612-4554-4 |
| work_keys_str_mv | AT bealsmichael propagationandinteractionofsingularitiesinnonlinearhyperbolicproblems |