Free Boundary Problems: Theory and Applications, Volume II (Chapman & Hall CRC Research Notes in Mathematics Series)

Cover......Page 1
Title: Free boundary problems: theory and Applications, VOLUME II......Page 2
ISBN 0-273 08590-5......Page 3
Contents of Volume I......Page 4
Contents of Volume II......Page 6
1. Some history......Page 10
3. Acknowledgements......Page 11
4. The general scheme of the Symposium and of the Proceedings......Page 12
One-phase problem......Page 14
Two-phase problem......Page 15
2. APPLICATIVE MOTIVATIONS......Page 16
3.1.1. Multidimensional situation......Page 17
Globa\'l continuity......Page 19
3.1.2. one-dimensional situation......Page 20
3.1.3. Degenerate Problems......Page 21
Non-local nonlineariti~s......Page 22
Space-periodicity......Page 23
problems with convection......Page 24
4. CHARACTERIZATION OF THE FREE BOUNDARY IN MULTIDIMENSIONAL PROBLEMS......Page 25
5. NUMERICAL TECHNIQUES......Page 26
6. A FEW OPEN PROBLEMS......Page 27
References......Page 28
References......Page 41
A BOSSAVIT: Stefan models for eddy currents in steel......Page 42
1.1. Induction heating of a cylindrical billet......Page 45
1.2. The electric equation: a periodic Stefan problem......Page 47
1.3. Numerical approach......Page 48
2.1. Models using h......Page 49
2.2. Models using a......Page 50
3. DIMENSION 3......Page 53
3 .1. A model problem......Page 54
3.2. Homogenization......Page 55
References......Page 56
INTRODUCTION......Page 58
1. THE MULTIPHASE STEFAN PROBLEM......Page 60
2. A VARIATIONAL FORMULATION FOR THE FREEZING INDEX......Page 62
3.1. Formulation of the approximation......Page 64
3. 2. Error estimate......Page 65
4. NUMERICAL APPLICATIONS......Page 67
References......Page 71
LA CAFFARELLI & L C EVANS: Continuity of the temperature in two-phase Stefan problems......Page 73
A. Graphs of Stefan type......Page 76
C. Fast diffusion......Page 77
D?Graphs of partially saturated Porous media type......Page 78
Graphs of type C and D......Page 80
3. BOUNDARY REGULARITY......Page 82
3.i) Variational boundary data......Page 83
3-ii) Dirichlet boundary data......Page 85
References......Page 87
1. UNICITY AND EXISTENCE OF SOLUTION OF PROBLEM 1......Page 90
2. REDUCTION TO A QUASI-VARIATIONAL INEQUALITY......Page 94
3. EXISTENCE OF THE SOLUTION OF PROBLEM 2......Page 96
References......Page 99
2.1. Classical formulation......Page 100
2.2. variational formulation......Page 102
3. EXISTENCE OF WEAK SOLUTION......Page 105
4. UNIQUESNESS OF WEAK SOLUTION......Page 109
References......Page 110
I INTRODUCTION......Page 112
II WEAK FORMULATION......Page 113
III A FIRST EXISTENCE RESULT......Page 115
V UNIQU!NESS......Page 121
VI ORDER OF CONVERGENCE ESTIMATE......Page 122
References......Page 123
2. PHYSICAL AND TECHNOLOGICAL APPLICATIONS......Page 124
Numerical methods......Page 147
APPENDIX 2: TO THE NUMERICAL SOLUTION OF THE INVERSE STEFAN PROBLEM by P. Jochum......Page 148
Two-phase Stefan problem:......Page 126
4. APPLICATION OF INVERSE FORMULATIONS OF BOUNDARY VALUE PROBLEMS......Page 127
4.1. Basic mathematical properties......Page 128
4.2. Problems involving unknown boundary data......Page 129
4.3. Other inverse problems......Page 133
4.4. Comments......Page 134
One-dimensional problems:......Page 135
Multi-dimensional problems......Page 138
6. FEEDBACK CONTROL......Page 139
7. COMMENTS......Page 140
References......Page 141
TWO dimensional Stefan-Problem......Page 150
References......Page 151
APPENDIX 3: ON A FREE BOUNDARY VALUE PROBLEM RELATED TO THE OPTIMAL STOPPING OF A DETERMINISTIC SYSTEM by I. Capuzzo Dolcetta and M. Matzeu.......Page 152
References......Page 155
1. INTRODUCTION......Page 156
2. A BOUNDARY VALUE PROBLEM WITH FIXED BOUNDARY......Page 157
3. THE DIFFERENTIABLE DEPENDENCE OF THE FREE BOUNDARY......Page 160
4. CONCLUDING REMARKS......Page 163
References......Page 164
ASPECTS OF MOVING BOUNDARY PROBLEMS IN ELECTROCHEMICAL MACHINING -McGeough, J. A.......Page 165
A COMPARISON OF COMPUTATIONS AND MODELLING IN ELECTROCHEMICAL MACHINING - E. B. Hansen......Page 173
THE MODELLING OF SOME MELTING PROBLEMS - R. S. Peckover......Page 174
The Hydrodynamic Limit......Page 176
Damkohler Number Asymptotics......Page 177
Activation Energy Asymptotics......Page 178
One-Dimensional Deflagration and Perturbation......Page 179
Reduction to a Parabolic System......Page 180
Flame tips......Page 181
Straining Flows......Page 182
Future Prospects......Page 183
References......Page 184
1. INTRODUCTION......Page 186
2. WEAK FORMULATIONS......Page 189
3. NUMERICAL SOLUTION......Page 192
4. RESULTS AND DISCUSSIONS......Page 194
References......Page 197
C MELLIOTI: A variational inequality formulation of a steady state electrochemical machining free boundary problem......Page 198
References......Page 204
1  INTRODUcriON......Page 206
2  NUMERICAL SOLUTION......Page 207
References......Page 208
1 INTRODUCI\'ION......Page 209
2 ? THE METHOD......Page 211
3. RESULTS AND DISCUSSION......Page 214
References......Page 217
II. VISCOUS FRICTION LAW......Page 219
III  VARIATIONAL FORMULATION......Page 220
V. PROOF OF THE THEOREM......Page 221
APPENDIX......Page 224
References......Page 226
Optimal Conductor Design......Page 227
References......Page 231
D KINDERLEHRER: A note on the variational method in contact problems......Page 232
2. VARIATIONAL INEQUALITY AND COMPLEMENTARITY CONDITIONS......Page 234
3. CAPACITY AND STABILITY......Page 238
References......Page 241
1. MECHANICAL BEHAVIOUR OF FROZEN SOILS......Page 242
2. INTERGRANULAR STRESSES IN FROZEN SOIL......Page 244
References......Page 252
1?INTRODUCTION......Page 254
2?SETTING OF THE PROBLEM......Page 255
3?ASYMPTOTIC EXPANSION AND CONSEQUENCES......Page 257
4?INDICATIONS ABOUT EXISTENCE AND UNIQUESNESS OF THE LOCAL PROBLEM......Page 259
5.1. The limit problem......Page 261
5.2. On the structure of the friction laws ~]/[10]:......Page 262
References......Page 263
1 GENERAL REMARKS......Page 265
2. THE FREE BOUNDARY INCLUSION METHOD WITH THE AID OF MONOTONICITY......Page 266
3. NUMERICAL EXAMPLE......Page 268
References......Page 271
1. THE H-METHOD FOR STEFAN PROBLEMS......Page 273
2. A GENERALIZED STEFAN PROBLEM - SUPERCOOLING AND SURFACE TENSION......Page 275
3. PHASE FIELD MODELS......Page 278
4. NUMERICAL APPROXIMATIONS......Page 281
References......Page 282
1. ONE DIMENSIONAL PROBLEMS......Page 283
2. PARTIAL DIFFERENTIAL EQUATIONS......Page 284
3. SOME OPEN PROBLEMS......Page 289
References......Page 290
J A NITSCHE: Finite element approximation to the one-phase Stefan problem......Page 294
References......Page 298
INTRODUCTION......Page 299
ONE-PHASE PROBLEMS......Page 301
EFFECT OF SAMPLE SIZE......Page 303
References......Page 305
1. REYNOLDS\' EQUATION......Page 306
2. THE VARIATIONAL INEQUALITY OF THE HYDRODYNAMIC LUBRIC:ATION WITH CAVITATION......Page 309
3. A PARTICULAR CASE......Page 311
4. HYDRODYNAMIC LUBRICATION WITH CAVITATION OF JOURNAL BEARINGS......Page 314
5. ASYMPTOTIC SOLUTIONS. THE INFINITELY LONG JOURNAL BEARINGS......Page 318
6. THE INFINITELY SHO:Rl\' JOURNAL BEARINGS......Page 323
7. DISCUSSION ON THE CONDITIONS OF TRANSITION......Page 325
References......Page 326
1. THE MODELS......Page 329
2. MULTIPLE EQUILIBRIA AND STABILITY......Page 331
3. SOME OF THE ASTRONOMICAL BACKGROUND......Page 333
5. SOME SOLUTIONS WITH PERIOD OF ONE YEAR......Page 334
References......Page 336
1. INTRODUCTION......Page 337
2. NOTATION AND RESULTS......Page 340
3. PROOF OF THEOREM 2.1.......Page 342
APPENDIX......Page 348
References......Page 349
A FRIEDMAN: Asymptotic estimates for variational inequalities......Page 351
References......Page 356
I. MULTISPECIES SYSTEM......Page 357
II. TRAVELLING FRONTS......Page 359
References......Page 364
INTRODUCTION......Page 365
I.1. Existence and uniqueness of solutions......Page 366
I. 2. Shape and smoothness of configurations, \'a priori\' estimates......Page 367
II.1. First approach: the operator a......Page 368
II.2. Second approach: S as an independent variable......Page 369
II.2.1. A priori estimates for problem (1\')......Page 370
II.2.2. A new variational approach......Page 371
References......Page 372
0. INTRODUCTION......Page 375
1. THE LOCAL PROBLEM......Page 376
References......Page 381
INTRODUCTION......Page 382
FORMULATION......Page 384
ANALYSIS......Page 388
RESULTS......Page 392
References......Page 393
THE PHYSICAL MODEL......Page 394
EXISTENCE RESULT......Page 397
CONSTRUCTION OF THE APPROXIMATE SOLUTION......Page 400
ESTIMATES ON \'DIE APPROXIMATE SOLtJTION......Page 401
CONVERGENCE......Page 402
References......Page 404