Floquet Theory for Partial Differential Equations:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1993
|
| Schriftenreihe: | Operator Theory: Advances and Applications
60 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-0348-8573-7 |
| Beschreibung: | Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267] |
| Umfang: | 1 Online-Ressource (XIV, 354 p) |
| ISBN: | 9783034885737 9783034896863 |
| DOI: | 10.1007/978-3-0348-8573-7 |
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| 500 | |a Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267] | ||
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Datensatz im Suchindex
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| discipline | Allgemeine Naturwissenschaft Mathematik |
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| id | DE-604.BV042422171 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:46Z |
| institution | BVB |
| isbn | 9783034885737 9783034896863 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857588 |
| oclc_num | 1184267359 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
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| physical | 1 Online-Ressource (XIV, 354 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series2 | Operator Theory: Advances and Applications |
| spellingShingle | Kuchment, Peter Floquet Theory for Partial Differential Equations Science (General) Science, general Naturwissenschaft Floquet-Theorie (DE-588)4317056-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4317056-0 (DE-588)4044779-0 |
| title | Floquet Theory for Partial Differential Equations |
| title_auth | Floquet Theory for Partial Differential Equations |
| title_exact_search | Floquet Theory for Partial Differential Equations |
| title_full | Floquet Theory for Partial Differential Equations by Peter Kuchment |
| title_fullStr | Floquet Theory for Partial Differential Equations by Peter Kuchment |
| title_full_unstemmed | Floquet Theory for Partial Differential Equations by Peter Kuchment |
| title_short | Floquet Theory for Partial Differential Equations |
| title_sort | floquet theory for partial differential equations |
| topic | Science (General) Science, general Naturwissenschaft Floquet-Theorie (DE-588)4317056-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Science (General) Science, general Naturwissenschaft Floquet-Theorie Partielle Differentialgleichung |
| url | https://doi.org/10.1007/978-3-0348-8573-7 |
| work_keys_str_mv | AT kuchmentpeter floquettheoryforpartialdifferentialequations |