03054nam 2200637 450 99646658720331620220511180356.03-540-69545-110.1007/BFb0093368(CKB)1000000000437345(SSID)ssj0000324318(PQKBManifestationID)12071110(PQKBTitleCode)TC0000324318(PQKBWorkID)10312530(PQKB)10242893(DE-He213)978-3-540-69545-5(MiAaPQ)EBC5610765(MiAaPQ)EBC6710548(Au-PeEL)EBL5610765(OCoLC)1079003254(Au-PeEL)EBL6710548(PPN)155205226(EXLCZ)99100000000043734520220511d1997 uy 0engurnn|008mamaatxtccrLarge-time behavior of solutions of linear dispersive equations /Daniel B. Dix1st ed. 1997.Berlin, Heidelberg :Springer-Verlag,[1997]©19971 online resource (XIV, 203 p.) Lecture Notes in Mathematics ;1668Bibliographic Level Mode of Issuance: Monograph3-540-63434-7 Includes bibliographical references and index.Laplace expansions, outer regions -- Expansion in the inner region, Matching -- Uniformly Valid Expansions for large time -- Special Results for Special Cases -- Applications: Self-similar asymptotic approximations; Sharp Ls decay estimates, Smoothing Effects; Asymptotic balance for large time; Asymptotic behavior for large x -- Reference -- Subject Index.This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed.Lecture notes in mathematics (Springer-Verlag) ;1668.Initial value problemsDifferential equations, LinearAsymptotic theoryAsymptotic expansionsInitial value problems.Differential equations, LinearAsymptotic theory.Asymptotic expansions.515/.353Dix Daniel Beach1959-61862MiAaPQMiAaPQMiAaPQBOOK996466587203316Large-time behavior of solutions of linear dispersive equations261828UNISA