Proceedings 'WASCOM 2003' 12th Conference on Waves and Stability in Continuous Media

Preface......Page 6
Conference Data......Page 12
TABLE OF CONTENTS......Page 14
1. Introduction: electric network equations......Page 21
2. Coupling of network and semiconductor equations......Page 23
3. Elliptic and parabolic multi-physics models......Page 25
References......Page 26
1. Introduction......Page 27
2. Presentation of the model and preliminary discussion......Page 28
3. Time-periodic solutions to the full model......Page 30
References......Page 32
1. Introduction......Page 33
2. The Boltzmann equation for semiconductors......Page 34
3. Moment equations......Page 35
5. Fluxes and surface terms......Page 38
6. Production terms......Page 39
7. Applications to the case of bulk Si......Page 43
References......Page 44
1. Introduction......Page 46
2. Mathematical preliminaries......Page 48
3. Analysis of the dynamics......Page 49
References......Page 51
1. Introduction......Page 52
2. Desch-Schappacher-Webb criterion and its consequences......Page 53
3. Chaos in linear kinetic models......Page 54
References......Page 57
1. Introduction......Page 58
2. The method......Page 59
3. POD for finite-dimensional dynamical systems......Page 62
4. Applications to Navier-Stokes equations......Page 63
5. Characterization of periodic behaviour......Page 65
6. Hopf bifurcation center manifold and normal form......Page 68
7. Concluding remarks......Page 70
References......Page 71
1. Introduction......Page 72
2. Mathematical formulation of the problems......Page 74
3. The numerical method......Page 76
4. Numerical results......Page 77
References......Page 79
1. Introduction......Page 80
2. Formulation of inverse problems for the source......Page 81
3. Numerical simulations and results......Page 83
References......Page 89
1. Introduction......Page 90
2. Kane models......Page 91
3. Derivation of Kane models......Page 92
References......Page 97
1. Introduction......Page 98
2. Wigner formulation of the Kane model......Page 99
3. Concluding remarks......Page 103
References......Page 104
1. Introduction......Page 105
2. Chemical reaction model......Page 106
References......Page 113
1. Introduction......Page 114
2. The generalized kinetic approach......Page 116
3. The general solution of the macroscopic approach......Page 118
References......Page 121
1. The model......Page 122
2. The Riemann Problem......Page 123
3. Numerical Methods......Page 124
4. Numerical Results......Page 125
References......Page 127
1. Introduction......Page 129
2. Basic equations and steady state solution......Page 130
3. Global Nonlinear Stability......Page 132
References......Page 134
1. Introduction......Page 136
2. Existence and regularity results......Page 139
References......Page 140
1. Introduction......Page 142
2. The reactive Euler equations......Page 144
3. The Riemann problem......Page 145
4. The numerical method......Page 148
5. Numerical results......Page 149
References......Page 152
1. INTRODUCTION......Page 153
2. M EVEN ODD/2q filling all |x| + |z| odd even fig3......Page 154
3. Half-Space M = (2p + 1)/5 Heavy Dodecagons figs4......Page 156
References......Page 158
1. Introduction......Page 161
2. General remarks and outlines......Page 162
3. R-H and Lax conditions......Page 164
References......Page 167
1. Introduction......Page 168
2. Hydro dynamical equations......Page 169
3. Soliton-like solutions......Page 170
4. Capillary fluid......Page 171
References......Page 172
1. Introduction : The entropy/entropy dissipation method......Page 173
2. Two examples : Fokker-Planck and Boltzmann kernels......Page 175
3. Degenerate setting......Page 178
4. The Fokker-Planck equation in a confining potential......Page 180
5. The Boltzmann equation in a bounded box with specular reflexion......Page 182
References......Page 184
1. Introduction......Page 186
2. The aggregated model......Page 187
3. The Chapman-Enskog procedure......Page 189
References......Page 191
2. Fading memory and thermodynamics......Page 192
3. Weak formulation and applications to linear viscoelasticity......Page 198
References......Page 203
1. Computation of the system equilibria......Page 205
2. Maximum entropy method......Page 208
4. Computation of the entropy of the system......Page 209
References......Page 210
1. Introduction......Page 211
2. Inhibitory effect of toxins......Page 213
3. Lethal effect of toxins......Page 216
4. Lethal effect of toxins and quorum sensing......Page 219
References......Page 222
1. Internal and external derivation with respect to a given hypersurface......Page 224
2. Regularly discontinuous functions and jumps up to the fourth order......Page 227
3. Jumps of order M: a general formula......Page 230
4. Examples......Page 231
References......Page 240
1. Introduction.......Page 241
2. Steady Unsteady and Perturbation Problems.......Page 243
3. Results for the Porous Medium......Page 244
4. Analogous Estimate for a Steady Diffusion Problem in a Right Cylinder......Page 247
References......Page 249
1. Introduction......Page 250
2. Reduction to canonical forms......Page 252
3. Exact solutions via differential constraints......Page 256
4. Conclusions and final remarks......Page 258
References......Page 260
1. Introduction......Page 261
2. Weak equivalence transformations ad classification......Page 262
3. Lie symmetries and solutions in a case of biological interest......Page 263
4. Numerical solutions of the PDEs......Page 265
References......Page 266
1. Introduction......Page 267
2. The balance energy equation......Page 268
3. Two embedding theorems......Page 269
4. L2 energy estimates......Page 270
5. Stability theorems......Page 271
References......Page 273
Thermocapillary Fluid and Adiabatic Waves Near its Critical Point......Page 274
1. Equations of motion of thermocapillary fluids......Page 275
2. Liquid-vapor interface near its critical point......Page 280
3. Weak discontinuity in conservative motions......Page 283
References......Page 287
1. Introduction......Page 289
2. Kinematics......Page 290
3. Dynamics......Page 292
References......Page 294
1. Introduction......Page 295
2. Preliminaries......Page 297
3. Solutions......Page 298
References......Page 300
1. Introduction and Basic Equations......Page 301
2. A Rational Hierarchy of Models......Page 306
3. Response in Some Homogeneous Deformations......Page 309
References......Page 311
1. Introduction......Page 315
2. The vectorial equation of motion......Page 316
3. Gimbals and wheels dynamic......Page 319
4. Feedback law......Page 320
References......Page 322
1. Introduction......Page 323
2. Control of Benard convection and finite dimensional approximation......Page 324
4. Time delayed control......Page 325
5. Conclusions and open problems......Page 327
References......Page 328
2. Low and high field mobilities......Page 329
References......Page 335
Noncanonical Poisson Brackets in Deformed Special Relativity......Page 336
References......Page 340
1. Introduction......Page 341
2. Rescaling and formulation of the problem......Page 343
3. Well-posedness......Page 345
4. Homogenization of a periodic network of parallel capillaries......Page 348
References......Page 353
1. Introduction......Page 354
2. The hydrodynamic equations......Page 355
3. The Numerical Method......Page 356
4. Numerical Results......Page 358
References......Page 360
1. Introduction......Page 361
2. Gibbs Paradox......Page 362
3. Boltzmann\'s Entropy in the Kinetic Theory of Gases......Page 363
4. A Jump to Conclusion. The Pseudo-Gibbs-Paradox......Page 365
5. Boltzmann\'s Entropy Eq.(3.7) as k ln W......Page 367
6. Conclusion......Page 370
References......Page 371
1. The stability problem......Page 372
2. Stabilizing effects in ODE......Page 375
3. Stability in a reaction-diffusion problem......Page 378
4. The Benard\'s problem......Page 381
References......Page 385
1. Basic equations.......Page 386
2. Simulation results.......Page 389
References......Page 391
1. Lie Group Analysis......Page 392
2. Remarkable Systems......Page 393
3. Monge-Ampere Equations......Page 395
4. Third Order Completely Exceptional Equations......Page 396
References......Page 398
1. Introduction......Page 400
2. Approximation procedure......Page 402
3. Reactive Navier Stokes equations......Page 403
4. Transport coefficients......Page 404
References......Page 405
1. Introduction......Page 406
2. On the symmetry condition......Page 408
3. On the further condition (13)......Page 411
References......Page 412
1. Introduction.......Page 413
2. Determination of the tensor Xi1...in j1...jn......Page 417
3. Proof of proposition 1.......Page 418
References......Page 419
1. The stochastic revised Enskog equation......Page 420
2. The transport coefficients and the equation of state......Page 422
3. The stochastic square-well kinetic equation......Page 425
References......Page 426
1. Introduction......Page 427
2. Kinetic aspects of the central limit theorem for stable laws......Page 429
3. The inelastic Kac model......Page 431
4. Steady states of infinite energy......Page 432
5. Existence and uniqueness of solutions......Page 434
6. Central limit theorem for inelastic Kac model......Page 435
7. Grazing collision limit and the fractional Fokker-Planck equation......Page 438
References......Page 439
1. Introduction......Page 441
2. Preliminaries......Page 442
3. Two weighted energy relations......Page 444
4. Energy inequalities......Page 445
5. Stability Criteria......Page 447
6. Longtime behaviour of the solutions of the porous medium and horizontal filtration equations......Page 451
References......Page 452
1. Introduction......Page 454
2. The mathematical model......Page 455
3. Equivalence transformations......Page 456
4. Symmetry classification via equivalence transformations......Page 458
References......Page 460
1. Balance Laws Systems Entropy and Generators......Page 461
2. Principal Subsystems......Page 462
4. Qualitative Analysis......Page 463
5. Mixtures of Fluids......Page 466
6. Entropy Principle and Thermodynamical Restrictions......Page 469
7. Constitutive Assumptions......Page 471
References......Page 473
1. Introduction......Page 475
2. Mathematical Model and Basic Assumptions......Page 476
3. Characteristic Speeds and Acceleration Waves......Page 477
4. Shock Waves......Page 478
References......Page 482
1. The moment\'s method in Extended Thermodynamics......Page 483
2. Analysis of the hyperbolicity zone......Page 485
References......Page 489
1. The Cellular Neural Network: An introduction......Page 490
2. The CNN simulation: Results.......Page 493
References......Page 494
1. Introduction......Page 495
2. Preliminaries......Page 497
3. Limiting behavior with a regular interaction rate......Page 498
4. Initial data in the class L1+ for ka |a| < 1......Page 499
References......Page 501
1. Introduction......Page 502
2. Stochastic volatility and transaction costs......Page 505
3. Utility maximization......Page 506
4. The asymptotic procedure......Page 508
5. Conclusions......Page 511
References......Page 513
1. Introduction......Page 514
2. The equations. Preliminary results......Page 516
3. Construction of Approximate Inertial Manifolds......Page 517
References......Page 519
1. Introduction......Page 520
2. 2D steady solution......Page 521
3. 3D steady solution......Page 523
4. Unsteady planar motion with H transverse......Page 524
References......Page 526
1. Introduction......Page 527
3. Perturbation equations......Page 528
References......Page 530
1. Introduction......Page 532
2. A new continuum model of crystalline solids......Page 533
3. Linear wave propagation......Page 536
4. Discussions......Page 541
References......Page 543
1. Introduction......Page 544
2. Partially invariant solutions......Page 545
3. The unsteady Navier-Stokes equations......Page 547
4. Some particular solutions of the Navier-Stokes equations......Page 548
References......Page 553
1. Introduction......Page 555
2. Hamiltonian Formulation......Page 557
3. Numerical Integration of NLS......Page 558
References......Page 560
1. Introduction......Page 561
2. Lie equivalence algebra and differential invariant......Page 562
References......Page 566
1. Introduction......Page 567
2. Field equations......Page 568
3. Acceleration waves......Page 569
4. Conclusions......Page 573
References......Page 574
1. Introduction......Page 575
2. The Green\'s Identity......Page 579
3. Using the Method of Characteristics......Page 580
4. Closed Loop Integral Curves......Page 582
References......Page 583
1. Start points......Page 584
2. Stability and Liapunov\'s functions......Page 585
3. Precompactness limiting equations and asymptotic stability......Page 586
4. Applications to the analytical mechanics......Page 588
References......Page 589