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Asymptotic expansions and summabilityapplication to partial differential equations /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Asymptotic expansions and summabilityby Pascal Remy.
其他題名:	application to partial differential equations /
作者:	Remy, Pascal.
出版者:	Cham :Springer Nature Switzerland :2024.
面頁冊數:	xiii, 246 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Summability theory.
電子資源:	https://doi.org/10.1007/978-3-031-59094-8
ISBN:	9783031590948$q(electronic bk.)

Asymptotic expansions and summabilityapplication to partial differential equations /
Remy, Pascal.

Asymptotic expansions and summabilityapplication to partial differential equations /[electronic resource] :by Pascal Remy. - Cham :Springer Nature Switzerland :2024. - xiii, 246 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23511617-9692 ;. - Lecture notes in mathematics ;2035..

- 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.

ISBN: 9783031590948$q(electronic bk.)

Standard No.: 10.1007/978-3-031-59094-8doiSubjects--Topical Terms:

199058
Summability theory.

LC Class. No.: QA295

Dewey Class. No.: 515.243

Asymptotic expansions and summabilityapplication to partial differential equations /
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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.
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