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Kuznetsov N., Mazya V., Vainberq B. Ч Linear Water Waves: A Mathematical Approach
Kuznetsov N., Mazya V., Vainberq B. Ч Linear Water Waves: A Mathematical Approach

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Ќазвание: Linear Water Waves: A Mathematical Approach

јвторы: Kuznetsov N., Mazya V., Vainberq B.

јннотаци€:

This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'


язык: en

–убрика: ћатематика/—имметри€ и группы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2002

 оличество страниц: 532

ƒобавлена в каталог: 24.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
A priori estimate      90
Abramowitz, M.      12 145 146 150 152 159 160 163 188 310 467
Acceleration caused by gravity      1 2 87 265 266 349 393 422 439
Airy function      283 286 287 293 297
Akilov, G.P.      61 371 385 388
Angell, T.S.      98 109 112 140
Aranha, J.A.P.      224 230
Artificial boundary      224 225
Assertion on continuity of solutions      53
Asymptotic behavior      28
Asymptotic formula      12 28 41 46 66 67 69 96 181 227 283 286 309 311 317 320 324 325 327 329Ч335 341Ч343 350Ч352 364Ч366 376Ч378 394 397 412 435 438 443 460 461 464 475 481 483
Asymptotic representation      283
Asymptotic, behavior      21 22 27 32 39 42 117 148 152 171 188 266 283 284 287 289Ч291 295 303 314 316 319 332 404 407 433 468 487 491
Asymptotics at infinity      25 327 341 343 362 379 381
Athanassoulis, G.A.      141 434
Aubin, J.ЧP.      105
Auxiliary integral identity      70 134 135 231 234
Axisymmetric, problem      97 122 130 140 142 143 158 212 213
Axisymmetric, structures      162
Azimuthal mode      143 163 164 188 189 212 213
Baar, J.J.M.      317
Bai,K.J.      113
Banach space      60 62 292 370
Banerjea, S.      98 213
Barber, N.F.      6
Barrier      98 164 165 170Ч172 213 260 262 488 489 493 495
Bauer      316
Beale, J.T.      6 10
Beam      417
BernoulliТs equation      3 436
Bessel function      12 25 26 41 132 133 159Ч161 163 186 188 231 232 259 502
Bessho, M.      316 416 418
Bhattacharya, R.N.      xii
Bipolar coordinates      201
Birman, M.S.      106 225 257
Bochner, S.      39 314
Bolton, W.E.      218
BonnetЧBen Dhia, A.ЧS.      220 223 229
Bottom      1 5 9 11 42 50 54 58 68Ч71 78 80 81 88 92Ч95 97 98 112 117 121 124Ч126 134 137 139 156 165 169 173 175 185 192 198 199 202 203 212 215Ч217 219 220 224Ч227 230 231 234 235 241 256 261 325 341 344 350 352 360 412 413 421 432 433 455 487 488 503
Bottom condition      352
Bottom movement      435 439 455
Bouligand, G.      433
boundary conditions      3 5 43 44 46 54 69 88Ч90 94 105 118 139 171 214 230 312 344 348 361 362 416 488 491
Brard, R.      16 418
Burago, Yu.D.      96
Buslayeva, M.V.      433
Callan, M.      256
Carleman, T.      65 96 103 375
Cauchy principal value      23 34 39 306 312
Cauchy problem for the Laplace equation      59 169 326 348 380 402 413 414
Cauchy Ч Poisson problem      4 7 433 460 477 487 491
Cauchy Ч Riemann equations      338 348 368Ч370
Cauchy, A.L.      xi
CauchyТs inequality      167 174
Chabat, B.V.      230 235
Chudinovich, I.Yu.      433
Circular cylinder      43 49 97 229 231 255 256 258 318 337 397 416 483 486 495 500 501
Circulation      16 360 365 398
Clarisse, J.ЧM.      317 433
Cliff      156 197 220 225 226
Colton, D.      53 96
Comparison method      228
Complete elliptic integral      41
Complex potential      307 434
Condition of the Kutta Ч Zhoukovsky type      416
Continuity equation      2 436
Corner point      51 60Ч63 65Ч67 170 171 362 403
Courant, R.      22
Crapper, G.D.      xi
Cross, R.H.      14
Cutoff      233 236 238Ч241 244 249 255 258 496
Cutoff function      278 366
Cylindrical wave      12 37
Davies, E.B.      256
Davis, A.M.J.      141
Dean, R.G.      6
Debnath, L.      xii 5
Deep water      11 12 15 16 21 37 39 40 42 46 68 69 76 80 121 124Ч127 130 143 158 175 185 192 204 205 211 213 229 230 232 239 241 255 265 305 316Ч318 351 353 359 362 398 411 415 450 451 466 495 500
Dern, J.C.      360
Dipole      177 178 180 239 407
DiracТs measure      21 22 94 281 313 459 475
Direct integral equation      54
Dirichlet Ч Neumann operator      104 106 107 426
Divergence theorem      14 23 70 103 228 234 239 351
Dobrokhotov, S.Yu.      433
Doppel, K.      98 141
Dynamic boundary condition      3
Eatock Taylor, R.      256
Edge waves      214Ч216 219 220 222 226 227 229 233 255 262 488Ч490 497 501 502
Eggers, K.W.H.      316 416
Ehrenmark, U.T.      223
ellipse      76 77 126
Energy      4 5 13 60 71 72 101 102 105 118 142 144 166 202 208 213 217 219Ч222 227 229 232 237 318 327 390 405 438 439 442 443 446 456 457 460 465^167 481
Energy conservation law      443 449 457 465
Energy norm      446 473
Error function      451 467
Essential norm      62 65 103 108 371 373 387
Euler, L.      xi
EulerТs constant      151 310
Euvrard, D.      316 434
Evans, D.V.      xvii 49 98 212Ч214 216 220Ч222 229 231Ч233 255Ч258 260Ч262
Exponential integral      150 406
Extended auxiliary integral identity      135 198 241
Fedoryuk.M.V.      291
Fernyhough, M.      232 262
Feshbach, H.      193 206
Feynman, R.P.      xi
FitzЧGerald, G.F.      97
Floating body      6 156 434 485 488 492 496 501
Flow of energy      13
Forward speed      265 349 361 393 395 417 490 501
Fourier coefficients      462 476 482 483
Fourier transform      21 24 48 141 223 268 269 274 280Ч282 313 317 423 425 450 465 473 474 480 489
Fox, D.D.      105
Fredholm operator      62 373
Fredholm theory      58 59
FredholmТs alternative      50 58 61 87 103 108 358 371 373 375 387 388 399 415
Free surface      1 3Ч5 7 9Ч11 15 17 22 39 42 48Ч50 54 56 69 70 87 88 92Ч95 99 100 105 112 113 116 117 123Ч126 130 131 134 136 137 139 142Ч145 157 162Ч165 169Ч173 177 179 185 188Ч191 193 196 198 203 205 208 209 212 215Ч217 219 224 231 232 234 238 239 241 244 245 248 249 252 261 265Ч267 283 287Ч289 309 311 316 344 349 358 363 364 370 403 407 410 412 417 421 422 426 432 433 435Ч437 442 443 451 455 456 460 464 465 468 486 490Ч492
Free surface, boundary condition      8 17 31 41 52 70 72 112 130 169 177 185 274 342 356 367
Free surface, elevation      4 7 365 370 442 443 455 456 459 468 479
Freeg surface      397
Friedman, A.      432
Friis, A.      141
Galerkin approximation      262
Gamma function      292
Garipov, R.M.      230 235 432 433
Geometric criteria of uniqueness      50
Gilbarg, D.      59 90 118 140 423 424 429
Gohberg, I.      55 359
Gradshteyn, I.S.      12 24 25 27 35 36 40Ч42 65 131 146 182 310 314 315 374 406 407 451 466
Greenspan, H.P.      222
GreenТs formula      51 69 92 101 103 106 122 124 127 166 167 324Ч326 330 352 366 367 379 383 388 400 428 449 456 481
GreenТs function      21Ч25 28 30 32 33 36Ч40 42 43 48Ч50 52 90 93 100 105 109Ч114 139 177 232 233 245 253 265Ч268 280 283 284 305 308 309 311 312 314Ч320 324 326 327 343 349 353 354 356 359 366 370 376 378 380 381 385 389 415
GreenТs representation      21 48 109Ч112 116 319 417
Grimshaw, R.H.      97 220 227 228 234
Groves, M.D.      218
Grue, J.      141
Gutmann, C.      359
H function      359
Hadamard, J.      433
Half-axis      56 83 142 147 149 150 184 245 270 274 297 313 407 409
Half-plane      38 66 114 177 194 200 209 232 237 270 283 287 306 307
Half-space      22 32 185 206 273 281 286 287 436 473
Hamdache, K.      17
Hankel function      12 13 36 131 159
Harmonic function      22 24 33 43 46 47 52 53 62 67 107 124 130 138 144 148 157 177 178 253 308 312 337 338 347 357 368 380 383 392 407 424 425 460
Haskind, M.D.(Khaskind)      xii 48 359
Havelock, T.H.      xi 48 238 239 316 417
Hazard, C.      14 98
Hearn,G.E.      110
Heaviside function      147 267 309 312 313 342 347 365
Helmholtz equation      117 255 491 503
Hermans, A.J.      xii 418
Hilbert space      446 486 489
Hilbert, D.      22 55 62 257 422
Hille, E.      254
Hochmuth,R.      141
Hogner, E.      316
Hou, T.Y.      6
Hsiao, G.C.      xii 98 109 112 141 418
Hulme, A.      48 76 97
Hurd, R.A.      262
Hypersingular operator      109 110 112
Impulsive pressure      433 435Ч438 448 451
Initial conditions      7 9 437 441 442 445 454 455 457 464 477
InitialЧboundary value problem      10 14 17 421 422 433 435 441 444 447 454 459 461 463 466 472 475 477 480
Integral, equation      50Ч61 65 87 88 96 98Ч100 102Ч104 107 109Ч113 115 116 121 122 232 233 255 262 318 321Ч323 331Ч333 336 341 345Ч348 357Ч359 370 375 380 399 417 485 487 491 492 494Ч496 499 501 502
Integral, operator      50Ч52 54 61 64 90 100 103 109 111 112 232 318 321 333 357 359 399 492
Integroalgebraic system      370Ч372 377 380 385Ч387 399 404 415
Inverse procedure      158 212 361 406 417
Invertibility theorem      55 61 62 65 96 101 103 321 323 359 373 377 399
Irregular frequency      140 494
Isakova, E.K.      433
Jacobian      89 200 210
Jami, A.      98 434
John, R.      xi xiv 5 8 10 48 99 100 116 117 120 121 126 134 136Ч140 143 164 176 177 179 180 189Ч192 195 205 208 231 238Ч242
Joly, P.      220 223 229
Jones, D.S.      113 217 229 230
Jump formula      311 322 332 337
Kakilis, P.D.      141
Kamotskii, I.V.      256
Kantorovich, L.V.      61 371 385 388
Keldysh, M.V.      317
Keller, J.B.      227 417
Kellogg, O.D.      53 56 357
Kelvin, Lord (Sir W.Thomson)      xi xiv 265 283 316
KelvinТs angle      283 285 287 288 291 295 316
KelvinТs source      283 316
Kenig, C.E.      96
Kinematic boundary condition      4
kinetic energy      4 68 105 116 165 167 173 177 186 196 362 363
Kirchgassner, K.      5
Kirchhoff, G.R.      xi
Kleinman, R.E.      98 109 110 112 113 141
Knife-like ship      417
Kochin, N.E.      xi 48 51 55 87 96 316 317 359 360
Komech, A.I.      219 220 222 223
Kondratyev, V.A.      96 101 364
Kopachevskiy, N.D.      105
Korobkin, A.A.      433
Kostyukov, A.A.      xii 316 317 359 360 418
Kozlov, V.A.      55 62 92 96 101
Krai, J.      96
Krein, S.G.      55 105 359
Kreisel, G.      97
Kress, R.      53 96
Kronecker delta      40 46 71 186 234
Kuttler, J.R.      105
Kuznetsov, N.G.      97 140 141 192 212Ч214 216 231 237 241 359 405 415 416 484
KuzТmina, V.M.      433
Lagrange, J.L.      xi
Lahalle, D.      359
Laitone, E.V.      xi xvi 5 48 227 315 316 359 360 418
Lamb, H.      xi 2 3 214 437
Laplace equation      3 24 34 41 46 47 50 70 72 88 96 118 119 167 185 216 274 281 339 356 357 362 436 462 476
Lau, S.M.      110 432
Lavrentiev, M.A.      230 235 317
Layer of variable depth      49 70 83 85 87 97 436 502
Le Blond, P.H.      214
Le Mehaute, B.      2 6
Least singular solution      397 416
Lee, S.W.      110 262
Lehman, R.S.      220
Lenoir, M.      14 48 98 141 317 416
Leppington, F.G.      141
Lesky, P.H.      218
Levine, H.      171
Levitin, M.      256 257
LeviЧCivita, T.      5
Lewy, H.      220
Liapis, S.      110
Licht, C.      10 14
Lighthill, M.J.      xi
Line source      21 244 305 317
Linearization      6Ч8
Linton, C.M.      xii xvii 98 192 213 228 231 232 255 260Ч262
Lipschitz condition      71 253 254
Liu, Y.W.      113
Livshits, M.L.      97 359
Local asymptotics      170 362 366 403 411
Lowengrub, J.S.      6
Ludwig, D.      141
Makrakis, G.N.      434
Mandal, B.N.      98 213
Maniar, H.D.      256
Martin, P.A.      114 115 140 141 232
Maskell, S.J.      434
MazТya, V.G.      48 49 54 55 62 92 96Ч98 101 165 169 213 231 235 283 316 317 359 415 416 433 484
McIver toroid      498
Mclver, M.      xvii 98 116 141 212 228 256 261
Mclver, P.      xii xvii 15 141 212 213 220 229 231Ч233 238 239 255 256
Mean value theorem      22 47 148
Mei, C.C.      xii
Merzon, A.E.      220 222 223 227
Method of stationary phase      290 291 296Ч298
Meyer, R.E.      227
Michell, J.H.      417
Mihlin, S.G.      53 55 56 96 357
Miles, J.W.      227
Mittag Ч LefflerТs theorem      36
Mittra, R.      262
Modified GreenТs function      113 115 491
Moiseev, N.N.      105
Moon pool      212
Morris, C.A.N.      49
Morse, M.      193 206
Motygin, O.V.      xvii 213 234 238 359 405 415 416
Mysak, L.A.      214 215
Nachbin, A.      484
Nakos, D.E.      417
Nalimov, V.I.      7
Nazarov, S.A.      96 101 256 484
Nekrasov, A.I.      5
Neumann condition      8 52 53 56 58 59 61 66 69 74 92 94 95 102 105 107 112 139 142 145 160 167 216 261 330 333 342 346 347 356 364 380 384 400 403 406 449 460 462 482
NeumannЧKelvin problem      16 283 284 311 313 318 319 323 324 326 337 341 342 347 349 358Ч362 395 397 398 403 405 406 411 416 417 487 493 497 498 500 501
Newman, J.N.      xii xvi 15 17 212 213 256 311 316 317 433
NgoZuyCan      105
No-flow condition      3 145 341 352 363 395 412 413
Noblesse, E.      316
Nodal line      138Ч140 146 148Ч156 161 179Ч181 407 410
Normal velocity      4 5 9
Null-field equations      115 495 496
Obstacle      4 14 21 44 50 51 65 68 98 116 121 122 125 126 142 144 169 216 231 256 421 493 495 496
Olver, F.W.J.      5 42
Ovsyannikov, L.V.      xii 5 7
Packham, B.A.      222
Pagani, C.D.      360 417
Palm.E.      141
Pamovski, L.      256
Papanicolaou, G.C.      484
Parker, R.      258
Parseval theorem      474
ParsevalТs equality      423 426 466
Parsons, N.      232
PascalТs snail      402
Perturbation procedure      7 17
Peters, A.S.      16 221 316
Petrovski, I.G.      63 254 321 357
Piecewise smooth contour      61 65 127
Pierotti, D.      360 417
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