LEADER 03868nam 22006255 450 001 9910869157103321 005 20251217133045.0 010 $a9783031590948$b(electronic bk.) 010 $z9783031590931 024 7 $a10.1007/978-3-031-59094-8 035 $a(MiAaPQ)EBC31511222 035 $a(Au-PeEL)EBL31511222 035 $a(CKB)32650215900041 035 $a(DE-He213)978-3-031-59094-8 035 $a(PPN)279809972 035 $a(EXLCZ)9932650215900041 100 $a20240702d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAsymptotic Expansions and Summability $eApplication to Partial Differential Equations /$fby Pascal Remy 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (248 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2351 311 08$aPrint version: Remy, Pascal Asymptotic Expansions and Summability Cham : Springer,c2024 9783031590931 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis book provides a comprehensive exploration of the theory of summability of formal power series with analytic coefficients at the origin of Cn, aiming to apply it to formal solutions of partial differential equations (PDEs). It offers three characterizations of summability and discusses their applications to PDEs, which play a pivotal role in understanding physical, chemical, biological, and ecological phenomena. Determining exact solutions and analyzing properties such as dynamic and asymptotic behavior are major challenges in this field. The book compares various summability approaches and presents simple applications to PDEs, introducing theoretical tools such as Nagumo norms, Newton polygon, and combinatorial methods. Additionally, it presents moment PDEs, offering a broad class of functional equations including classical, fractional, and q-difference equations. With detailed examples and references, the book caters to readers familiar with the topics seeking proofs or deeper understanding, as well as newcomers looking for comprehensive tools to grasp the subject matter. Whether readers are seeking precise references or aiming to deepen their knowledge, this book provides the necessary tools to understand the complexities of summability theory and its applications to PDEs. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2351 606 $aMathematical analysis 606 $aMathematical physics 606 $aAnalysis 606 $aMathematical Physics 606 $aExpansions asimptòtiques$2thub 606 $aEquacions en derivades parcials$2thub 606 $aSumabilitat$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical analysis. 615 0$aMathematical physics. 615 14$aAnalysis. 615 24$aMathematical Physics. 615 7$aExpansions asimptòtiques 615 7$aEquacions en derivades parcials 615 7$aSumabilitat 676 $a515.353 700 $aRemy$b Pascal$01743650 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910869157103321 996 $aAsymptotic Expansions and Summability$94171903 997 $aUNINA