Fedoryuk (Ed) - Partial Differential Equations V. Asymptotic Methods for Partial Differential Equations (Encyclopedia Math. Sci., Springer)(244s).pdf

文档介绍：VI--~
bartial Differential
Equations V
Asymptotic Methods
for Partial Differential Equations
J-y” y,t. ?
With 21 Figures I 4
Springer
Encyclopaedia of
Mathematical Sciences
Volume 34
Editor-in-Chief: RX Gamkrelidze
Contents
I. Equations with Rapidly Oscillating Solutions
M. V. Fedoryuk
1
II. Asymptotic Expansion as t 4 00 of the Solutions
of Exterior Boundary Value Problems
for Hyperbolic Equations
and Quasiclassical Approximations
B. R. Vainberg
53
III. The Higher-Dimensional WKB Method
or Ray Method.
Its Analogues and Generalizations
V. M. Babich
91
IV. Semiclassical Asymptotics of Eigenfunctions
V. F. Lazutkin
133
V. The Boundary Layer
A. M. Il’in
173
VI. The Averaging Method
for Partial Differential Equations (Homogenization)
and Its Applications
N. S. Bakhvalov, G. P. Panasenko, and A. L. Shtaras
211
Author Index
241
Subject Index
245
I. Equations
with Rapidly Oscillating Solutions
M. V Fedoryuk t
Translated from the Russian
by S. A. Wolf
Contents
. Foreword ............................................... 3
51. Local Asymptotics. ........................................... 3
. Formal Asymptotic Solutions ............................. 3
. The Hamilton-Jacobi Equation and Hamilton’s Equations .... 6
. The Cauchy Problem for the Hamilton-Jacobi Equations ..... 6
. The Transport Equations. ................................ 9
. Supplement ............................................. 11
$2. Lagrangian Manifolds ......................................... 15
. Isotropic Manifolds ...................................... 15
. Symplectic Geometry .................................... 16
. Canonical Transformations ............................... 18
53. Passing to the pRepresentation ................................ 20
. Pseudodifferential Operators .............................. 20