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- catalog abstract "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.".
- catalog contributor b10542896.
- catalog created "c1997.".
- catalog date "1997".
- catalog date "c1997.".
- catalog dateCopyrighted "c1997.".
- catalog description "Includes bibliographical references (p.[194]-197) and index.".
- catalog description "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.".
- catalog description "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.".
- catalog extent "xiv, 203 p. ;".
- catalog identifier "3540634347 (pbk. : acid-free paper)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1668.".
- catalog isPartOf "Lecture notes in mathematics ; 1668".
- catalog issued "1997".
- catalog issued "c1997.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog subject "510 s 515/.353 21".
- catalog subject "Asymptotic expansions.".
- catalog subject "Differential equations, Linear Asymptotic theory.".
- catalog subject "Differential equations, partial.".
- catalog subject "Initial value problems.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1668 QA347".
- catalog tableOfContents "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.".
- catalog title "Large-time behavior of solutions of linear dispersive equations / Daniel B. Dix.".
- catalog type "text".