Free Boundary Problems: v. 1: Theory and Applications (Chapman & Hall CRC Research Notes in Mathematics Series)

Cover\0......Page 1
Title: Free boundary problems: theory and applications, VOLUME I\0......Page 2
ISBN 0-273-08589-1\0......Page 3
Contents of Volume I\0......Page 4
Contents of Volume II\0......Page 6
1. Some history\0......Page 10
3. Acknowledgements\0......Page 11
4. The general scheme of the Symposium and of the Proceedings\0......Page 12
References\0......Page 13
J NORBURY: Free boundary problems of fluid mechanics\0......Page 14
References\0......Page 17
Hydrodynamic flows - flow through an orifice\0......Page 19
The method of variable finite elements\0......Page 20
Viscous flows - the drawing problem\0......Page 22
References\0......Page 24
M A BOUDOURIDES: Stability of a free boundary hydrodynamical flow\0......Page 26
References\0......Page 29
l. THE TWO DIMENSIONAL PROBLEM\0......Page 30
2. FREE-SURFACE AND BOUNDARY CONDITIONS\0......Page 31
3. KELVIN SOURCE\0......Page 33
4. THE MATHEMATICAL PROBLEM\0......Page 34
5  EXISTENCE, UNIQUENESS, AND REPRESENTATION FORMULA\0......Page 35
principle of the method. Formal study and uniqueness\0......Page 36
Representation formulas\0......Page 37
Existence theorem\0......Page 38
References\0......Page 40
Compactness theorem\0......Page 42
2. THE CAPILLARY TUBE\0......Page 43
3. LIQUID DROPS\0......Page 46
Existence theorem for pendent drops\0......Page 47
4. ROTATING FLUIDS\0......Page 48
Fundamental lemma\0......Page 49
References\0......Page 50
1 . INTRODUCTION\0......Page 52
Inclusion Theorem\0......Page 53
Under-Over Theorem\0......Page 55
3. APPLICATIONS TO FLUID FLOWS\0......Page 56
4. AXISYMMETRIC EXTENSIONS\0......Page 58
References\0......Page 60
B TURKINGTON: Steady flow with vorticity\0......Page 61
References\0......Page 64
THE STATIONARY DAM PROBLEM\0......Page 65
1. Stationary problem\0......Page 68
7. The non-steady problem\0......Page 78
References\0......Page 80
1. INTRODUCTION\0......Page 82
2.1. Local solutions\0......Page 83
2.5. Theorem\0......Page 84
2.9. Super- and subsolutions\0......Page 85
2.12. To give an idea of our results\0......Page 86
3.5. Remark\0......Page 87
References\0......Page 88
1  INTRODUCTION\0......Page 90
2  A WEAK FORMULATION OF PROBLEM ( 1) - ( 5)\0......Page 92
3. EXISTENCE\0......Page 94
4. UNIQUENESS\0......Page 97
References\0......Page 100
1 STATEMENT OF THE PROBLEM\0......Page 101
2. TWO USEFUL LEMMAS\0......Page 102
3. S3-CONNECTED SOLUTIONS\0......Page 104
4. UNIQUENESS OF S3 -CONNECTED SOLUTION\0......Page 105
References\0......Page 109
1. THE DAM PROBLEM WITH HORIZONTAL LAYERS\0......Page 111
2. HOK>GENIZATION OF THE VARIATIONAL INEQUALITY\0......Page 113
3. CONVERGENCE OF THE FREE BOUNDARY\0......Page 115
References[1] Alt, H. w.\0......Page 117
1. CLASSICAL FORMULATION OF THE PROBLEM\0......Page 118
2  FORMULATION OF\' THE VARIATIONAL INEQUALITY AND UNIQUENESS\0......Page 119
3. EXISTENCE OF THE SOLUTION OF PROBLEM 2. 1.\0......Page 122
References\0......Page 124
2. DIFFERENTIAL EQUATION FORMULATION AND EXTENSION\0......Page 125
3  FIRST SOLUTION APPROACH FORMULATION\0......Page 127
4. SECOND SOLUTION APPJIDACH FORMULATION\0......Page 130
5. THIRD SOLUTION APPROACH FORMULATION\0......Page 132
6. RESULTS\0......Page 133
References\0......Page 137
2. PRELIMINARIES\0......Page 138
3. CONTINUITY OF THE FREE BOUNDARY\0......Page 141
4  ASYMPTOTIC BEHAVIOUR OF THE FREE BOUNDARY\0......Page 145
References\0......Page 146
D GARONSON: Nonlinear diffusion problems\0......Page 148
A. NONSTATIONARY FILTRATION IN PARTIALLY SATURATED POROUS MEDIA\0......Page 156
B. DECAY OF SOLUTIONS OF A DEGENERATE NONLINEAR DIFFUSION EQUATION\0......Page 158
References\0......Page 161
1. THE POROUS MEDIUM EQUATION\0......Page 163
2. THE INITIAL VALUE PROBLEM IN ONE SPACE DIMENSION\0......Page 164
3. PROBLEMS IN MORE THAN ONE SPACE DIMENSION\0......Page 171
References\0......Page 172
S KAMIN & P ROSENAU: Propagation of thermal waves in inhomogeneous media\0......Page 173
References\0......Page 179
J LVAZQUEZ: Large time behaviour of the solutions of the one-dimensional porous media equation\0......Page 180
1. MODEL SOLUTIONS\0......Page 181
2 ? GENERAL SOLUTIO\0......Page 182
3. TWO INVARIANTS\0......Page 183
4. COMPARISON BY SHIFTING\0......Page 184
Shifting Comparison Principle\0......Page 185
5. THE LARGE-TIME BEHAVIOUR OF THE SOLUTIONS\0......Page 186
5.3. Optimal rates of convergence\0......Page 188
References\0......Page 189
1. MATHEMATICAL MODEL\0......Page 191
2. NUMERICAL SCHEME\0......Page 192
3. RESULTS AND DISCUSSION\0......Page 195
1. Asymptotic behaviour of redistribution in the unsaturated region\0......Page 197
3. The velocity of infiltrating wet front\0......Page 198
4. Effect of Pending\0......Page 199
5. Effect of Rainfall Intensity\0......Page 200
6. Effect of the Discontinuity of Soil Texture\0......Page 201
7. Effect of thin layer\0......Page 202
References\0......Page 203
2. THE APPLICATIONS\0......Page 204
3.2.1. Conservation of the mass of solid and liquid water\0......Page 205
3.2.3. Conservation of the energy of the water and the skeleton\0......Page 206
3. 3. THE CONSTITUTIVE LAWS\0......Page 207
3. 5. THE THERMAL MODEL\0......Page 208
3.5.1. The quasi static thermal model\0......Page 209
3. 6. THE HYDRAULIC AND THERMAL MODEL\0......Page 210
4.1. THERMAL MODEL\0......Page 213
4.2.2. The variational formulation\0......Page 214
4.2.3. Some functional spaces\0......Page 216
4.2.4. Mathematical results (13]\0......Page 217
4.2.5. Proof outlines of theorems 1 and 2\0......Page 218
5. THE HORIZONTAL DISTRIBUTION OF THE PER~IAFROST\0......Page 219
References\0......Page 220
Determination of the horizontal distribution of permafrost and of itsmaximum depth during seasonal thaw by Xu Xiaozu (Lanzhou Institute ofGlaciology and Cryopedology - P.R.C.)\0......Page 222
References\0......Page 224
Symbols\0......Page 225
PHYSICAL NATURE IN FROST PROCESSES\0......Page 226
THE APPROXIMATE CALCULATION OF FROST PROCESSES Frost penetration depth and amount of migrating water\0......Page 229
Unfrozen water content and amount of frost heave\0......Page 231
CONCLUSIONS\0......Page 234
References\0......Page 235
1. INTRODUCTION\0......Page 236
2 THE MATHEMATICAL PROBLEM\0......Page 237
3. EXISTENCE AND UNIQUENESS THEORY\0......Page 239
4. CONCLUDING REMARKS\0......Page 243
J ROCKENDON: Generalised phase-change problems\0......Page 244
References\0......Page 249
I.1. Physical equations\0......Page 250
I.2. Mathematical formulation\0......Page 252
!.3. Case of a mushy region\0......Page 253
II. STUDY OF A DISCRETIZED PROBLEM\0......Page 254
II.1 A result of existence\0......Page 255
II.2. Numerical algorithm\0......Page 256
III.3. Numerical results\0......Page 257
References\0......Page 259
2.1. Formulation\0......Page 261
B. Slow Descent\0......Page 263
3.1. Formulation and Melting Regimes\0......Page 266
3.2. Premelting\0......Page 269
3.3. High Heat Flux: Q >> 1\0......Page 270
References\0......Page 274
1. INTRODUCTION\0......Page 276
2. ENTROPY MAXIMIZATION\0......Page 279
3. ENERGY OF SURFACE TENSION\0......Page 282
4. NUMERICAL TREATMENT\0......Page 286
References\0......Page 287
INTRODUCTION\0......Page 288
1. MODELLING THE MUSHY REGION IN A BINARY ALLOY CAPABLE OF FORMING A CONTINUOUS SET OF SOLID SOLUTIONS\0......Page 289
A. Equations of heat transfer within the solid-liquid phase of the mushy region\0......Page 290
F. Initial conditions in Gsf\0......Page 291
G. Conditions on the boundaries of Gsf\0......Page 292
2. MODELLING THE MUSHY REGION IN BINARY ALLOYS CAPABLE OF FORMING A SIMPLE EUTECTIC MIXTURE AND IN MONOCOMPONENT MEDIUft. PASSAGE TO THE ONE TEMPERATUREFORMALISM\0......Page 293
References\0......Page 295
INTRODUCTION - PERSPECTIVES\0......Page 296
THE STATEMENT OF MELTING OR SOLIDIFICATION PROBLEMS\0......Page 297
Convection in the Molten Phase\0......Page 299
The Behavior of Multi-Component Systems\0......Page 300
CONCLUDING REMARKS\0......Page 303
References\0......Page 304
2. THE 1 GAMMA 1 METHOD: FRONT TRACKING ON A FIXED MESH IN TWO DIMENSIONS\0......Page 306
3. CONSERVATION FORM OF THE ISOTHERM MIGRATION METHOD (IMM)\0......Page 309
4. RESULTS FOR TEST PROBLEMS\0......Page 311
5. DISCUSSION AND CONCLUSIONS\0......Page 316
ACKNOWLEDGEMENTS\0......Page 317
References\0......Page 318
I. INTRODUCTION\0......Page 319
II. STATEMENT OF THE MATHEMATICAL PROBLEM\0......Page 321
III. A BRIEF INTRODUCTION TO SIMPLE TWO COMPONENT PHASE DIAGRAMS\0......Page 322
IV. OUR \"PHLOGISTON FORMULATION\"\0......Page 325
V. THE FINITE DIFFERENCE SCHEME\0......Page 329
VI  NUMERICAL EXPERIENCE WITH THE MODEL\0......Page 332
References\0......Page 333