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Full 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.
Contents
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.
