Large-time Behavior of Solutions of Linear Dispersive Equations

Daniel B. Dix (auth.)3540634347, 9783540634348

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.

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Table of contents :
Laplace expansions, outer regions….Pages 1-74
Expansion in the inner region, matching….Pages 75-95
Uniformly valid expansions as t→∞ ….Pages 96-113
Special results for special cases….Pages 114-154
Applications….Pages 155-193