03648nam a22005175i 4500 978-3-031-59094-8 DE-He213 20251030112608.0 cr nn 008mamaa 240702s2024 sz | s |||| 0|eng d 9783031590948 978-3-031-59094-8 10.1007/978-3-031-59094-8 doi QA299.6-433 PBK bicssc MAT034000 bisacsh PBK thema Remy, Pascal. author. aut http://id.loc.gov/vocabulary/relators/aut 79863 Asymptotic Expansions and Summability [electronic resource] : Application to Partial Differential Equations / by Pascal Remy. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIII, 246 p. 28 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 1617-9692 ; 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. Mathematical analysis. 64178 Mathematical physics. Analysis. Mathematical Physics. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031590931 Printed edition: 9783031590955 Lecture Notes in Mathematics, 1617-9692 ; 2351 75434 https://doi.org/10.1007/978-3-031-59094-8 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 61259 61259