LEADER 03054nam 2200637 450 001 996466587203316 005 20220511180356.0 010 $a3-540-69545-1 024 7 $a10.1007/BFb0093368 035 $a(CKB)1000000000437345 035 $a(SSID)ssj0000324318 035 $a(PQKBManifestationID)12071110 035 $a(PQKBTitleCode)TC0000324318 035 $a(PQKBWorkID)10312530 035 $a(PQKB)10242893 035 $a(DE-He213)978-3-540-69545-5 035 $a(MiAaPQ)EBC5610765 035 $a(MiAaPQ)EBC6710548 035 $a(Au-PeEL)EBL5610765 035 $a(OCoLC)1079003254 035 $a(Au-PeEL)EBL6710548 035 $a(PPN)155205226 035 $a(EXLCZ)991000000000437345 100 $a20220511d1997 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLarge-time behavior of solutions of linear dispersive equations /$fDaniel B. Dix 205 $a1st ed. 1997. 210 1$aBerlin, Heidelberg :$cSpringer-Verlag,$d[1997] 210 4$dİ1997 215 $a1 online resource (XIV, 203 p.) 225 1 $aLecture Notes in Mathematics ;$v1668 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-63434-7 320 $aIncludes bibliographical references and index. 327 $aLaplace 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. 330 $aThis book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1668. 606 $aInitial value problems 606 $aDifferential equations, Linear$xAsymptotic theory 606 $aAsymptotic expansions 615 0$aInitial value problems. 615 0$aDifferential equations, Linear$xAsymptotic theory. 615 0$aAsymptotic expansions. 676 $a515/.353 700 $aDix$b Daniel Beach$f1959-$061862 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466587203316 996 $aLarge-time behavior of solutions of linear dispersive equations$9261828 997 $aUNISA