Waves and Stability in Continuous Media: Proceedings of the 15th Conference on WASCOM 2009

CONTENTS......Page 10
Preface......Page 6
Organizing Committees......Page 8
1. Network models for electric circuits......Page 16
2. Distribuited models for semiconductor devices......Page 17
3. Coupling condition......Page 18
4. Main result......Page 19
References......Page 21
2. The model......Page 22
3. Nonlinear model: numerical results......Page 25
References......Page 29
1. Introduction......Page 30
2. Coordinates and field equations......Page 31
3. The solution......Page 32
4. The temperature definition......Page 33
References......Page 35
1. Introduction and outline of the problem......Page 36
2. Hyperbolic tumor growth model......Page 38
3. An hyperbolic model for the hantavirus infection......Page 40
References......Page 42
1. Introduction......Page 43
2. Kinetic model with taxation and redistribution......Page 44
3. Numerical results......Page 46
References......Page 48
1. Introduction......Page 49
2. Model equations and boundary data......Page 50
3. Numerical results and comparison between models......Page 52
4. Conclusions......Page 53
References......Page 54
1. Introduction......Page 55
2. Method......Page 56
3. Application to 2D-Boussinesq equation......Page 58
References......Page 60
1. The Li and Muldowney's method for global stability......Page 61
2. Basic ideas of the method......Page 62
3. Some three and four dimensional epidemic models......Page 63
References......Page 66
1. Introduction......Page 67
2. The semiclassical transport model......Page 68
3. Quantum transport model: the Wigner equation......Page 69
References......Page 72
1. Introduction......Page 73
2. Penetrative convection driven by a quadratic density law......Page 74
References......Page 76
1. Introduction......Page 78
2. Penetrative convection driven by a quadratic density law......Page 79
References......Page 81
1. Introduction......Page 83
2. Governing equations......Page 84
3. Stability analysis......Page 87
References......Page 88
1. Introduction......Page 89
2. Recursion Techniques: a Tool to construct Solutions of the Noncommutative KdV Hierarchy......Page 90
3. Scalar and matrix KdV hierarchies: Explicit solution formulae......Page 91
4. Some Explicit Solutions of the Matrix KdV Hierarchy......Page 93
References......Page 94
M. C. Carrisi, S. Pennisi A Comparison Between the Macroscopic Approach and the Generalized Kinetic Approach in Extended Thermodynamics......Page 96
1. Proof of proposition 1......Page 97
2. Proof of proposition 2 and 3......Page 98
References......Page 101
1. Introduction......Page 102
2. Macroscopic framework......Page 103
3. The detonation wave structure......Page 104
4. Numerical results......Page 105
References......Page 107
1. Introduction......Page 108
3. Characteristic Cauchy problem for quasilinear wave equations.......Page 109
4. The case of Einstein equations.......Page 111
5. Adapted null coordinates.......Page 112
6. C1 constraint.......Page 113
6.1. Solution of the C1 constraint.......Page 114
7. CA and Co constraints.......Page 115
8.2. Local geometric uniqueness.......Page 116
References......Page 117
1. Introduction......Page 118
2. Lie symmetries and Riemann problem......Page 119
3. Approximate Lie symmetry approach......Page 120
References......Page 123
1. Introduction......Page 124
2. Singularity analysis......Page 125
3. Method to find all the elliptic solutions......Page 128
4. Elliptic and degenerate elliptic solutions, generic case......Page 129
4.1. Elliptic and degenerate elliptic solutions, one series......Page 130
4.2. Elliptic and degenerate elliptic solutions, two series......Page 132
References......Page 134
1. Introduction......Page 135
2. Main assumptions and preliminary estimates......Page 136
3. Stability and asymptotic stability of the null solution uo......Page 140
References......Page 142
1. Introduction......Page 143
2. Reduction to autonomous form......Page 144
3. Hyperbolic model and approximate Lie symmetries......Page 145
4. An approximately invariant solution......Page 146
Bibliography......Page 147
1. Introduction......Page 149
2. Basic equations......Page 150
4. The criterion......Page 151
5. Simulations and results......Page 152
References......Page 154
1. Introduction......Page 155
2. The Benard problem of a rotating mixture......Page 156
3. The rotating magnetic Benard problem......Page 158
References......Page 160
1. Introduction......Page 161
2.1. Benard system for a binary mixture......Page 162
2.3. Linear instability equations......Page 164
3.1. Note on fixed heat fluxes......Page 165
3.3. Results for Benard system......Page 166
3.4. Results for porous media......Page 168
4. Conclusions......Page 169
References......Page 170
1. Introduction......Page 171
2. Fundamental lemmas......Page 172
4. Schrodinger equations......Page 174
5. Wave Equation......Page 176
References......Page 177
1. Diffusion-driven instability......Page 178
2. Weakly nonlinear analysis: the supercritical case......Page 180
3. The Fourier-Galerkin approximation......Page 181
4. The subcritical case......Page 183
Appendix A. The Fourier-Galerkin procedure......Page 185
References......Page 186
1. Introduction......Page 188
2. Statement of the problem......Page 189
3. Unsteady Separation Process......Page 191
4. Singularity tracking method for Navier-Stokes......Page 193
5. Conclusion......Page 195
References......Page 196
1. Introduction......Page 197
2. Geometrical properties of the Reynolds tensor evolution......Page 199
3. Conclusion......Page 204
References......Page 205
1. Introduction......Page 206
2. Simple relativistic fluid......Page 208
3. The central hypothesis for a fluid mixture......Page 209
4. Dalton's law case......Page 211
5. Isobaric case......Page 212
6. Weak discontinuities......Page 214
References......Page 218
2. Relativistic flow model......Page 221
3. Discontinuities......Page 223
4. Application......Page 225
References......Page 227
1. Introduction......Page 229
2. The MHD model and the equilibria......Page 230
3. Numerical results......Page 233
4. Conclusions and further developments......Page 237
References......Page 238
1. Introduction......Page 239
2. Group classification......Page 240
3. Similarity reductions......Page 241
References......Page 243
1. Introduction......Page 245
2. Collocation method......Page 247
4. Scalar equation......Page 248
5. A first order method......Page 249
6. A second and third order method......Page 250
7. Higher order methods......Page 252
9.1. Tests on the well-balanced property......Page 253
9.2. Tests on the order of accuracy......Page 254
References......Page 255
1. Introduction......Page 257
2. The exact and the discretized transport equations......Page 258
3. Evaluation of the error and concluding remarks......Page 260
References......Page 262
1. Introduction......Page 263
2. Solution of the problem......Page 266
References......Page 268
1. Introduction......Page 269
2. The hydrodynamical models......Page 270
3. A comparison between the two models in the case of bulk silicon......Page 271
4. Conclusions and acknowledgments......Page 273
References......Page 274
1. Introduction......Page 275
2. The nonlinear elastodynamic system......Page 276
3. A Backlund transformation for model stress-strain laws......Page 277
3.1. Single action on stress-strain laws......Page 278
3.2. Itemtive action on stress-stmin laws......Page 280
3.3. Coalescence of the Backlund parameters......Page 281
4. Two-Pulse interaction......Page 282
References......Page 284
1. Introduction......Page 285
2.1. The law of the corresponding states......Page 288
2.2. Thermodynamic stability and phase transition......Page 289
References......Page 292
2. Outlines of hyperbolic systems of conservation laws......Page 294
3. Shock waves and Rankine-Hugoniot conditions......Page 296
4. The admissibility of shock waves......Page 297
5. Analysis of the shock admissibility in the van der Waals fluid......Page 300
References......Page 302
2. Numerical results......Page 304
3. Conclusions......Page 308
References......Page 311
1. Introduction......Page 312
2. Model......Page 313
2.1. Laminar regime......Page 316
References......Page 317
1. Introduction......Page 318
2. Equivalence of  -prolongations......Page 319
2.1.  -Equivalence of  -symmetries and first integrals......Page 320
2.2.  -Equivalence of Lie point symmetries......Page 322
References......Page 323
1. Introduction......Page 324
2. Analytical solutions for a channel with double opened ends......Page 325
4. Results......Page 328
References......Page 329
1. Introduction......Page 330
2. On a Theory by Sinai and Yakhot......Page 331
3. A Blob-Driven Form of Convection......Page 332
References......Page 335
1. A reduced linear system for the stability of ternary systems of O.D.Es......Page 336
2. Reduction of the L2-stability of a ternary nonlinear reaction diffusion system of P.D.Es to the stability of a ternary linear system of O.D.Es.......Page 342
References......Page 346
1. The Model......Page 347
2. Reduction to a Riemann Problem......Page 348
References......Page 352
2. Axi-symmetric I3-moments equations......Page 353
3. Symmetries and Optimal System of Lie Subalgebras......Page 354
4. H -invariant solutions......Page 355
Bibliography......Page 358
1. Introduction......Page 359
2. From particles to fluid dynamic description of flocking......Page 361
3. Numerical experiments......Page 365
References......Page 366
1. The Wigner approach and QHD system......Page 368
2. The QMEP with a total energy scheme......Page 371
References......Page 373
1. Introduction......Page 374
2. Laminar flows in bitumen......Page 376
References......Page 379
1. Introduction......Page 380
2. Stability......Page 383
References......Page 388