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Rauch J. — Partial differential equations
Rauch J. — Partial differential equations

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Название: Partial differential equations

Автор: Rauch J.

Аннотация:

From the preface:
I think that one learns more from pursuing examples to a certain depth, rather than giving a quick gloss over an enormous range of topics. For this reason, many of the equations discussed in the book are treated several times. At each encounter, new methods or points of view deepen the appreciation of these fundamental examples.
I have made a conscious effort to emphasize qualitative information about solutions, so that students can learn the features that distinguish various differential equations. Also the origins in applications are discussed in conjunction with these properties. The interpretation of the properties of solutions in physical and geometric terms generates many interesting ideas and questions.
It is my impression that one learns more from trying the problems than from any other part of the course. Thus I plead with readers to attempt the problems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Corrected

Год издания: 1999

Количество страниц: 266

Добавлена в каталог: 15.11.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$B^{s}_{tan}$      216
$C^{\infty}(R: \mathscr{S}(R^{d}))$      101
$C^{\infty}(x)$      227
$C^{\infty}_{0}(\Omega)$      248
$H^{-1}(\Omega)$      191
$H^{1}(\Omega)$      192
$H^{s}(R^{d})$      89
$H^{s}(x)$      165 187 225
$H^{s}(\Omega)$      225
$T_{x}$, $T_{x}^{*}$      28
$\delta^{h}_{v}$      220
$\mathscr{D}^{'}(\Omega)$      248
$\mathscr{E}(\Omega)$      248
$\mathscr{E}(\Omega)$, metric for      254
$\mathscr{E}^{'}(\Omega)$      253
$\mathscr{F}$      64
$\mathscr{F}^{*}$      67
$\mathscr{P}(\Omega)$      248
$\mathscr{R}$      69
$\mathscr{S}(R^{d})$      61
$\mathscr{S}^{'}(R^{d})$      74
$\overset{.}{H}^{1}(x)$      228
$\overset{.}{H}^{1}(\Omega)$      184
$\partial^{n}$      12
$\sigma_{\lambda}$      66
$\tau_{h}$      66 250
Acoustic waves      117 see
Airy equation      139ff 150
Burgers' equation      20ff 31 55ff 140
Cauchy — Kowaleskaya, theorem      §1.3—§1.8 230
Cauchy — Riemann equations      4 15 81 §3.8 124 144
Characteristic(s)      30 40 §1.9 125 215
Characteristic(s), curves      3 19 21
Characteristic(s), lines      2 30
Characteristic(s), surfaces      30 31
Characteristic(s), variety      31 95
Coercive      189 193 195 225
Comparison theorem      141 243
Conormal      30 216
Conormal space      30
Conormal variety      30
Convolution      §2.5 252 256
Cotangent space      29
Critical point      178 180
D      26
d'Alembert's formula      43ff §4.5
Descent, method of      §4.8
Dilation $\sigma_{\lambda}$      66 77 139
Dirac's delta function      249
Dirichlet problem      118 Ch.
Dirichlet's principle      178ff
Discontinous dependence      121 124 130 157
dispersion      103 105 107 149 150
Dissipation      120 215
distribution      248ff Ch.
Domain of determinacy      2 3 43ff 152 161
Domain of influence      2 3 43ff 152 161
Duhamel's principle      §3.11 §4.9
Eigenfunction expansions      70 201 §5.7
Eikonal equation      30
Elliptic equations and operators      1 6 31 42 54 81 96 106 172 191 Ch.
Elliptic regularity theorem      80—81 201 226
Elliptic regularity theorem, boundary      229ff
Elliptic regularity theorem, interior      227ff 239
Elliptic regularity theorem, tangential      §5.8
Ellipticity constant      189
Energy method      114 116 120 139 140 191
Euler equation      174 190 193
Fixed point equation      10 205
Fourier transform      §2.2ff
Frechet space      63 123
Fredholm alternative, for elliptic boundary value problems      §5.6 244
Fundamental solution      85 86 104 §4.2
Generalized Schwartz inequality      90 108 111
Generalized solution      104 §3.5 119 212
Greens function      85 86 §4.2
Group velocity      99 102 149 150
Hadamard — Petrowsky condition      §3.10 134 139 177
Harmonic function      17 81 157 175 176 238—239
Hausdorff — Young inequality      86
Heat equation      12 13 16 40 81 §3.6 §3.7 131 133 134 §4.2 §4.3 172ff 177ff 196 211ff 215
Heisenberg's uncertainty principle      97 98 99 105
Hodge theory      194ff 216 228
Holmgren's uniqueness theorem      16 §1.7 98 111 124
Holmgren's uniqueness theorem, global      §1.8 99 126
Holmgren's uniqueness theorem, semiglobal      39
Holomorphic function      5 17 81 144 236
Huygen's principle      160 162 164 165
Huygen's principle, generalized      165
Hyperbolic equations      1 96 127 162 228
Initial value problem      Ch. 1 Ch. Ch.
Laplace equation      12 15 81 131 157
Laplace — Beltrami operator      188 216
Lax duality theorem      90 111
Linearization      20 22 23 26 175
Loss of derivatives      131 156 157 161
Maximum principles      Cor. 4.3.4 172 §5.10 §5.11
Mean curvature      174 176 246
Mean value property      176 236 238ff
Measure(s)      141 164
Measure(s), Fourier transform of      82
Method of characteristics      19 131
Minimal surface      174 246
Monotonicity      161 165
Natural boundary condition(s)      194 196
Neumann problem      188 191 193 206 224—225 244
Noncharacteristic      18 19 23 25 30 32 40 §1.8 124 127
Nonstationary phase      149 150 166
Null solutions      41 98 111 §3.9
Order, of a distribution      249
Orthogonal invariance      86 153 154
Orthogonal transformation      70
Paley — Wiener theorem      86 122
Parabolic equations      13 96 106 107 163 211ff
Peter — Paul inequality      182
phase velocity      99 102 150
Poisson kernel      176
Propagator      134 Ch.
Propagator, heat      113 §4.2 §4.3
Propagator, Schroedinger      103 §4.2 §4.3
Propagator, wave      118 §4.2 §4.5 §4.7 §4.8 §4.9
Push forward      216 220
Quasi-linear trick      116 246
Radiation problems      §4.9
Rarefaction wave      56 140
Real analytic function      5 8 11 17 24 144
Reflection of waves      152
Reflection operator      69 70 84 251
Regular boundary point      228
Rellich compactness theorem      202
Riesz — Thorin convexity theorem      72 142
Robin problem/boundary condition      196 244
Schroedinger's equation      §3.2 §3.3 §3.4 §3.5 126 131 134 §4.2 §4.4 212
Self-similar      58 60 139 140
Separation of variables      207 211—214
Shock waves      6 54 59
sing supp      165
Smoothing property      143 212 215
Sobolev embedding theorem      93 184 187 210 228 231
Sobolev spaces      §2.6
Sound waves      21 57 117
Subharmonic function      179 235
Support      248 253
Symbol of a differential operator      §1.6
Tangent space      28 30
Taylor's theorem      136
Tempered distributions      §2.4ff
Tempered distributions, convergence      75
Trace, at boundary      196 198 200
Translation, $\tau_{h}$      66 77 250
Transpose of a differential operator      34 252
Transpose of a linear operator      34 76 251
Wave equation, damped or with friction      120 180 212 214
Wave equation, wave operator      12 31 43ff §3.7 131 133 136 §4.2 §4.5 §4.6 §4.7 §4.8 §4.9 212
Weak well-posed      131 132
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