03435nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001600188072002300204072001500227100008200242245013300324250001800457264006900475300004500544336002600589337002600615338003600641347002400677490005300701505050800754520130501262650003402567650002602601650001402627650002602641710003402667773002602701776003602727776003602763830006002799856004602859912001402905912001502919912001402934999001702948978-3-031-59094-8DE-He21320251030112608.0cr nn 008mamaa240702s2024    sz |    s    |||| 0|eng d  a97830315909489978-3-031-59094-87 a10.1007/978-3-031-59094-82doi 4aQA299.6-433 7aPBK2bicssc 7aMAT0340002bisacsh 7aPBK2thema1 aRemy, Pascal.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97986310aAsymptotic Expansions and Summabilityh[electronic resource] :bApplication to Partial Differential Equations /cby Pascal Remy.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIII, 246 p. 28 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Mathematics,x1617-9692 ;v23510 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.  aThis 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. 0aMathematical analysis.964178 0aMathematical physics.14aAnalysis.24aMathematical Physics.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303159093108iPrinted edition:z9783031590955 0aLecture Notes in Mathematics,x1617-9692 ;v235197543440uhttps://doi.org/10.1007/978-3-031-59094-8  aZDB-2-SMA  aZDB-2-SXMS  aZDB-2-LNM  c61259d61259