Asymptotic expansions and summability: application to partial differential equations
This book provides a comprehensive exploration of the theory of summability of formal power series with analytic coefficients at the origin of Cn, aiming to apply it to formal solutions of partial differential equations (PDEs). It offers three characterizations of summability and discusses their app...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2024]
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| Schriftenreihe: | Lecture notes in mathematics
Volume 2351 |
| Schlagworte: | |
| Zusammenfassung: | This book provides a comprehensive exploration of the theory of summability of formal power series with analytic coefficients at the origin of Cn, aiming to apply it to formal solutions of partial differential equations (PDEs). It offers three characterizations of summability and discusses their applications to PDEs, which play a pivotal role in understanding physical, chemical, biological, and ecological phenomena. Determining exact solutions and analyzing properties such as dynamic and asymptotic behavior are major challenges in this field. The book compares various summability approaches and presents simple applications to PDEs, introducing theoretical tools such as Nagumo norms, Newton polygon, and combinatorial methods. Additionally, it presents moment PDEs, offering a broad class of functional equations including classical, fractional, and q-difference equations. With detailed examples and references, the book caters to readers familiar with the topics seeking proofs or deeper understanding, as well as newcomers looking for comprehensive tools to grasp the subject matter. Whether readers are seeking precise references or aiming to deepen their knowledge, this book provides the necessary tools to understand the complexities of summability theory and its applications to PDEs |
| Beschreibung: | xiii, 244 Seiten Illustrationen, Diagramme |
| ISBN: | 9783031590931 |
Internformat
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| 245 | 1 | 0 | |a Asymptotic expansions and summability |b application to partial differential equations |c Pascal Remy |
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| 490 | 1 | |a Lecture notes in mathematics |v Volume 2351 | |
| 505 | 8 | |a - Part I Asymptotic expansions -- Taylor expansions -- Gevrey formal power series -- Gevrey asymptotics -- Part II Summability -- k-summability: definition and first algebraic properties -- First characterization of the k-summability: the successive derivatives -- Second characterization of the k-summability: the Borel-Laplace method -- Part III Moment summability -- Moment functions and moment operators -- Moment-Borel-Laplace method and summability -- Linear moment partial differential equations | |
| 520 | |a This book provides a comprehensive exploration of the theory of summability of formal power series with analytic coefficients at the origin of Cn, aiming to apply it to formal solutions of partial differential equations (PDEs). It offers three characterizations of summability and discusses their applications to PDEs, which play a pivotal role in understanding physical, chemical, biological, and ecological phenomena. Determining exact solutions and analyzing properties such as dynamic and asymptotic behavior are major challenges in this field. The book compares various summability approaches and presents simple applications to PDEs, introducing theoretical tools such as Nagumo norms, Newton polygon, and combinatorial methods. Additionally, it presents moment PDEs, offering a broad class of functional equations including classical, fractional, and q-difference equations. With detailed examples and references, the book caters to readers familiar with the topics seeking proofs or deeper understanding, as well as newcomers looking for comprehensive tools to grasp the subject matter. Whether readers are seeking precise references or aiming to deepen their knowledge, this book provides the necessary tools to understand the complexities of summability theory and its applications to PDEs | ||
| 650 | 4 | |a Summability theory | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Sommabilité | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 776 | 0 | |c Original | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-59094-8 |
| 830 | 0 | |a Lecture notes in mathematics |v Volume 2351 |w (DE-604)BV000676446 |9 2351 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035132080 | |
Datensatz im Suchindex
| _version_ | 1806685177460555776 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Remy, Pascal |
| author_GND | (DE-588)1336259736 |
| author_facet | Remy, Pascal |
| author_role | aut |
| author_sort | Remy, Pascal |
| author_variant | p r pr |
| building | Verbundindex |
| bvnumber | BV049791308 |
| classification_rvk | SI 850 |
| contents | - Part I Asymptotic expansions -- Taylor expansions -- Gevrey formal power series -- Gevrey asymptotics -- Part II Summability -- k-summability: definition and first algebraic properties -- First characterization of the k-summability: the successive derivatives -- Second characterization of the k-summability: the Borel-Laplace method -- Part III Moment summability -- Moment functions and moment operators -- Moment-Borel-Laplace method and summability -- Linear moment partial differential equations |
| ctrlnum | (OCoLC)1449545129 (DE-599)BVBBV049791308 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV049791308 |
| illustrated | Illustrated |
| indexdate | 2024-08-07T00:07:31Z |
| institution | BVB |
| isbn | 9783031590931 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035132080 |
| oclc_num | 1449545129 |
| open_access_boolean | |
| owner | DE-188 DE-83 |
| owner_facet | DE-188 DE-83 |
| physical | xiii, 244 Seiten Illustrationen, Diagramme |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Remy, Pascal (DE-588)1336259736 aut Asymptotic expansions and summability application to partial differential equations Pascal Remy Cham, Switzerland Springer [2024] © 2024 xiii, 244 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics Volume 2351 - Part I Asymptotic expansions -- Taylor expansions -- Gevrey formal power series -- Gevrey asymptotics -- Part II Summability -- k-summability: definition and first algebraic properties -- First characterization of the k-summability: the successive derivatives -- Second characterization of the k-summability: the Borel-Laplace method -- Part III Moment summability -- Moment functions and moment operators -- Moment-Borel-Laplace method and summability -- Linear moment partial differential equations This book provides a comprehensive exploration of the theory of summability of formal power series with analytic coefficients at the origin of Cn, aiming to apply it to formal solutions of partial differential equations (PDEs). It offers three characterizations of summability and discusses their applications to PDEs, which play a pivotal role in understanding physical, chemical, biological, and ecological phenomena. Determining exact solutions and analyzing properties such as dynamic and asymptotic behavior are major challenges in this field. The book compares various summability approaches and presents simple applications to PDEs, introducing theoretical tools such as Nagumo norms, Newton polygon, and combinatorial methods. Additionally, it presents moment PDEs, offering a broad class of functional equations including classical, fractional, and q-difference equations. With detailed examples and references, the book caters to readers familiar with the topics seeking proofs or deeper understanding, as well as newcomers looking for comprehensive tools to grasp the subject matter. Whether readers are seeking precise references or aiming to deepen their knowledge, this book provides the necessary tools to understand the complexities of summability theory and its applications to PDEs Summability theory Differential equations, Partial Sommabilité Équations aux dérivées partielles Original Erscheint auch als Online-Ausgabe 978-3-031-59094-8 Lecture notes in mathematics Volume 2351 (DE-604)BV000676446 2351 |
| spellingShingle | Remy, Pascal Asymptotic expansions and summability application to partial differential equations Lecture notes in mathematics - Part I Asymptotic expansions -- Taylor expansions -- Gevrey formal power series -- Gevrey asymptotics -- Part II Summability -- k-summability: definition and first algebraic properties -- First characterization of the k-summability: the successive derivatives -- Second characterization of the k-summability: the Borel-Laplace method -- Part III Moment summability -- Moment functions and moment operators -- Moment-Borel-Laplace method and summability -- Linear moment partial differential equations Summability theory Differential equations, Partial Sommabilité Équations aux dérivées partielles |
| title | Asymptotic expansions and summability application to partial differential equations |
| title_auth | Asymptotic expansions and summability application to partial differential equations |
| title_exact_search | Asymptotic expansions and summability application to partial differential equations |
| title_full | Asymptotic expansions and summability application to partial differential equations Pascal Remy |
| title_fullStr | Asymptotic expansions and summability application to partial differential equations Pascal Remy |
| title_full_unstemmed | Asymptotic expansions and summability application to partial differential equations Pascal Remy |
| title_short | Asymptotic expansions and summability |
| title_sort | asymptotic expansions and summability application to partial differential equations |
| title_sub | application to partial differential equations |
| topic | Summability theory Differential equations, Partial Sommabilité Équations aux dérivées partielles |
| topic_facet | Summability theory Differential equations, Partial Sommabilité Équations aux dérivées partielles |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT remypascal asymptoticexpansionsandsummabilityapplicationtopartialdifferentialequations |