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...
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| Váldodahkki: | |
|---|---|
| Searvvušdahkki: | |
| Materiálatiipa: | Elektrovnnalaš E-girji |
| Giella: | eaŋgalasgiella |
| Almmustuhtton: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
|
| Preanttus: | 1st ed. 2024. |
| Ráidu: | Lecture Notes in Mathematics,
2351 |
| Fáttát: | |
| Liŋkkat: | https://doi.org/10.1007/978-3-031-59094-8 |
| Fáddágilkorat: |
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| 100 | 1 | |a Remy, Pascal. |e author. |0 (orcid)0000-0002-7305-9340 |1 https://orcid.org/0000-0002-7305-9340 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Asymptotic Expansions and Summability |h [electronic resource] : |b Application to Partial Differential Equations / |c by Pascal Remy. |
| 250 | |a 1st ed. 2024. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2024. | |
| 300 | |a 1 online resource (XIII, 246 p. 28 illus.). | ||
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| 337 | |a computer |b c |2 rdamedia | ||
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| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
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| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2351 | |
| 505 | 0 | |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. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
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| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Analysis. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031590931 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031590955 |
| 830 | 0 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2351 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-59094-8 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||