Overview
- Self-contained presentation of the summability in the framework of formal power series with analytic coefficients
- Simply introduces the (new) theory of moment partial differential equations
- Presents different technical methods through various supplements and includes simple examples
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2351)
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Keywords
- Asymptotic Expansions
- Summability
- Formal Power Series
- Divergent Power Series
- Inhomogeneous Partial Differential Equation
- Nonlinear Partial Differential Equation
- Moment Partial Differential Equation
- Sequences, Series, Summability
- Several Complex Variables and Analytic Spaces
- Dynamical Systems
About this book
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.
Authors and Affiliations
About the author
Pascal Remy is a research associate at the Laboratoire de Mathématiques de Versailles, at the University of Versailles Saint-Quentin (France). His main interest is the theory of summation of divergent formal power series (including Gevrey estimates, summability, multi-summability, and Stokes phenomenon). His research extends to applications such as formal solutions of meromorphic linear differential equations, partial differential equations and integro-differential equations, both linear and nonlinear.
Bibliographic Information
Book Title: Asymptotic Expansions and Summability
Book Subtitle: Application to Partial Differential Equations
Authors: Pascal Remy
Series Title: Lecture Notes in Mathematics
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Softcover ISBN: 978-3-031-59093-1Due: 20 July 2024
eBook ISBN: 978-3-031-59094-8Due: 20 July 2024
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 232
Number of Illustrations: 28 b/w illustrations