Index 361
definition variable coefficient, 47
images, method of, 30–33
inequality of stationary phase, 106
influence curve, 79–83
integration by parts, justification, 61
inviscid compressible fluid dynamics, xv
Keller’s blowup theorem, 249
Klein–Gordon equation, 14, 19, 73, 78,
146, 246–257
Kreiss matrix theorem, xii, 88
lagrangian manifold, 213
Lax parametrix, 177–195
Liouville
Liouville number, 312
Liouville’s theorem, 238, 311
Littlewood–Paley decomposition, 109,
115, 222, 254
maximally dispersive, 92, 104, 242–246
Maxwell’s equations, xiv
characteristic variety, 67
circular and elliptical polarization, 73
eikonal equation, 154
introduction, 44–46
plane waves, 72
propagation cone, 68
rotation of polarization, 288–289
self phase modulation, 287–288
microlocal
analysis, xi, xviii
elliptic regularity theorem, xviii,
136–140
propagation of singularities theorem,
177–195
applied to stabilization, 195–205
Moser’s inequality, 224, 325
Hs,
284
nondegenerate phase, 182
nondispersive, 99
nonstationary phase, xii
and Fourier integral operators,
180–188
and group velocity, 16–20
and resonance, 293, 324
and the stationary phase inequality,
121–122
observability, xviii
operator
pseudodifferential, xii, 136, 186
transposed, 134
oscillations
creation of, 310
homogeneous, 302, 336–338
oscillatory integrals, 180–188
partial inverse
for a single phase, 155
multiphase
on quasiperiodic profiles, 307
on trigonometric series, 306
of a matrix, 117
perturbation theory, 239
for semisimple eigenvalues, 117–119,
164
generation of harmonics, 262–263
quasilinear, 239
semilinear, 227–230
small oscillations, 259–262
phase velocities, 74, 145
piecewise smooth
definition d = 1, 10
function, wavefront set of, 140
solutions for refraction, 38
solutions in d = 1, 11
plane wave, 17, 142–143
polarization
in nonlinear geometric optics, 268
linear, circular, and elliptical, 73
of plane waves, 72
rotation of axis, xviii, 288
polyhomogeneous, 182
prinicipal symbol, 64
profile equations
quasilinear, 302–314
semilinear, 265–275, 314–315
projection (a.k.a. averaging) operator
E, 267–275
propagation cone, 64–71, 75
propagation of singularities, xviii, 1
d = 1 and characteristics, 10–11
d = 1 and progressing waves, 12–16
using Fourier integral operators,
177–195
pulse, see wave
purely dispersive, 99–100
quasiclassical limit of quantum
mechanics, xvii, 149–151, 160–161,
278
Previous Page Next Page