Daniel B. Dix

Large-Time Behavior of Solutions of Linear Dispersive Equations

• Broschiertes Buch

Produktbeschreibung

This book provides a thorough description of the fundamentals and applications in this field. Basic concepts such as the optical and thermal properties of tissue, the various types of tissue ablation, and optical breakdown and its related effects are treated in detail. Special attention is given to mathematical tools (Monte Carlo simulations, the Kubelka--Munk theory etc.) and approved techniques (photodynamic therapy, laser-induced interstitial thermotherapy etc.). The part on applications reviews clinically relevant methods in modern medicine using the latest references. The last chapter covers today's standards of laser safety, with a careful selection of essential guidelines published by the Laser Institute of America. Numerous research photographs, illustrations, tables and comprehensive summaries make this book a useful guide for graduate students, scientists, and medical practitioners.

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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.

Produktdetails

• Lecture Notes in Mathematics 1668
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-63434-8
• 1997.
• Seitenzahl: 228
• Erscheinungstermin: 18. September 1997
• Englisch
• Abmessung: 235mm x 155mm x 13mm
• Gewicht: 346g
• ISBN-13: 9783540634348
• ISBN-10: 3540634347
• Artikelnr.: 09203126

Inhaltsangabe

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.