Asymptotic Expansions and Summability : Application to Partial Differential Equations

Pascal Remy

ISBN 10: 3031590937 / ISBN 13: 9783031590931

Editore: Springer Nature Switzerland, Springer International Publishing Jul 2024, 2024

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783031590931

Dati bibliografici

• Titolo: Asymptotic Expansions and Summability : Application to Partial Differential Equations
• Editore: Springer Nature Switzerland, Springer International Publishing Jul 2024
• Data di pubblicazione: 2024
• Lingua: Inglese
• ISBN 10: 3031590937
• ISBN 13: 9783031590931
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 15 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 15 millimetri di profondità
• Peso: 400 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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.