This volume considers the most recent advances in various topics in partial differential equations. Many important issues such as evolution problems, their asymptotic behavior and their qualitative properties are addressed. The quality and completeness of the articles make this book both a source of inspiration and reference for future research.
Author(s): Michel Chipot, Chang-Shou Lin, Dong-ho Tsai
Series: Proceedings of the International Conference on Nonlinear Analysis
Publisher: World Scientific
Year: 2008
Language: English
Pages: 268
City: Hackensack, NJ
CONTENTS......Page 8
Preface......Page 6
1. Introduction......Page 10
2. Statement of the result......Page 13
3. Completed relay operator......Page 15
4. Proof of Theorem 2.1......Page 16
References......Page 19
1. Introduction......Page 20
2. A first upper-bound......Page 25
3. A key proposition......Page 30
4. Proof of the lower-bound......Page 38
5. A refined upper-bound and the convergence result......Page 48
References......Page 51
1. Introduction......Page 52
2. A preliminary estimate......Page 53
3.1. The case where the growth of u is controled......Page 54
4. The case of the Laplace operator......Page 64
References......Page 73
1. Solid-liquid phase transitions......Page 76
2. Enthalpy formulation of the Stefan problem......Page 77
3. Phase field equations with convection......Page 80
References......Page 84
1. Introduction......Page 86
2. Various Concepts......Page 87
3. Typical results......Page 90
4. Ideas of proofs......Page 93
4.1. The proof of Theorem 3.3 (Part 1)......Page 95
4.2. The proof of Theorem 3.3 (Part 2)......Page 96
5. Some examples......Page 100
Acknowledgement.......Page 102
References......Page 103
1. Introduction......Page 104
2. Main transport result......Page 111
3. Correlated and uncorrelated heads in a three state system......Page 115
References......Page 119
1. Introduction......Page 122
2. Existence and uniqueness of a global solution......Page 124
3. Asymptotic behavior of u; v and w......Page 127
4. Nonexistence of a traveling wave solution......Page 129
5. Behavior of solutions for large 0......Page 131
References......Page 133
1. Introduction......Page 134
2. Motion of admissible polygons by crystalline curvature......Page 135
3. Beyond the singularities......Page 138
4. Almost convexity phenomena......Page 140
5. Discussion......Page 141
Acknowledgment......Page 142
References......Page 143
1. Introduction and Results......Page 144
2. Investigation of the linearized problem......Page 149
3. Sketch of Proofs......Page 153
References......Page 155
1. Introduction......Page 158
2. Main results......Page 160
3. Proof of main theorems......Page 164
4. Application to obstacle problems......Page 167
5. Application to problems with non-local constraints......Page 172
References......Page 178
1. Introduction......Page 180
2. Proof of Theorem 1.1......Page 183
3. Proof of Theorem 1.2......Page 185
References......Page 188
Introduction......Page 190
1. Statement of main results......Page 192
2. Well-posedness of solutions......Page 197
3. Periodic stability......Page 201
4. Applications......Page 203
References......Page 204
1. Introduction......Page 206
2. Prerequisites on Lorentz spaces......Page 209
3. Existence and uniqueness of principal eigenvalue......Page 211
4. Global bifurcation......Page 220
References......Page 224
1.1. Action......Page 226
1.2. Field equations for Gowdy symmetric spacetimes......Page 227
2. Global existence......Page 229
3. Initial singularity......Page 230
References......Page 231
1.1. Interfaces driven by reaction-diffusion equations......Page 234
1.2. Reaction-di usion with convection......Page 235
2. Planar Waves......Page 236
3.1. When codim P 1......Page 238
3.2. When s( ) 0......Page 241
4.1. Symmetric nonlinearity......Page 243
References......Page 245
1. Introduction......Page 246
2. Preliminaries......Page 249
3. Proofs......Page 251
References......Page 252
1. Introduction......Page 254
2. Assumptions and main result......Page 257
3. Original problems (P) and (OP)......Page 258
4. Approximating problems (P) and (OP)......Page 259
5. Necessary condition of optimal control for (OP) ......Page 262
References......Page 268
