Equadiff 9: Conference on Differential Equations and their Applications : Proceedings

Cover......Page 1
Preface......Page 2
Table of Contents......Page 3
 Introduction......Page 6
 Preliminaries......Page 7
Sufficient conditions on asymptotic stability......Page 9
Sufficient conditions for instability......Page 14
Examples......Page 15
Introduction......Page 22
Interpolation theory for grid functions......Page 23
Main result......Page 26
Convergence towards the sharp interface model......Page 34
Conclusion......Page 39
Blazhievskiy......Page 42
Introduction......Page 43
Introduction......Page 48
Extension of the perturbation problem......Page 49
Spaces of nonresonance solutions......Page 50
Regularisation of the singular perturbed problem......Page 51
Formalism of construction of solution of extended problem......Page 53
Asymptotic correctness of iterated problems......Page 55
Estimation of the last part of the asymptotic of a solution......Page 56
Introduction......Page 58
Results......Page 61
Introduction......Page 66
Evolution formulation of the plasticity BVP......Page 67
Example of analysis of plasticity models......Page 69
Computational method......Page 71
Numerical results......Page 74
Conclusion......Page 76
Introduction......Page 78
Scattering Problems......Page 79
Herglotz thermoelastic function......Page 81
Dense properties of the far field patterns......Page 83
Chrastina......Page 88
A note to proofs [3]......Page 89
Nonlinear dispersions......Page 90
The moving frames method [2]......Page 92
On the Darboux transformation [4]......Page 94
The Laplace coframe......Page 95
Example......Page 96
Introduction......Page 98
Ordinary Differential Equations......Page 100
Fractional-Order Functional Differential Equation......Page 101
Fractional-Order Evolution Equations......Page 102
Fractional-Order Diffusion-Wave Equation......Page 103
Introduction......Page 106
Linear parameter dependence......Page 107
Nonlinear parameter dependence......Page 110
Application of the PRM to a reaction-diffusion equation......Page 112
Francu......Page 116
Basic elements......Page 117
Stop and Play operator......Page 119
Ishlinskii operators......Page 121
Homogenization problem......Page 124
Homogenized operator......Page 126
Introduction......Page 128
Methods and technical difficulties......Page 129
Aims and preliminary results......Page 131
Hayashi and Hirata......Page 136
Karch......Page 142
Introduction......Page 144
Existence of Smooth Inertial Manifolds in a Set Q......Page 148
Overflowing Invariant Manifolds......Page 150
Proof of Theorem 8......Page 154
Some Comparison Theorems for Two-point Boundary Value Differential Inequalities......Page 156
Uniqueness and Estimates of U_0......Page 163
The Graph Transformation G_0......Page 166
Invariance and Exponential Tracking Properties of M......Page 168
Existence and Properties of G_1, G_2......Page 169
Introduction......Page 172
Auxiliary lemmata......Page 173
Main Theorems......Page 180
Introduction......Page 186
Recent history - a partial survey......Page 187
The size condition and some applications......Page 190
Decomposition of imbeddings......Page 193
Classical Formulation of the Problem......Page 198
Some Function Spaces and Their Properties......Page 199
Weak Formulation of the Problem......Page 200
The Frechet Derivative of Operator N......Page 201
Local Properties of Operator N......Page 202
Formulation of the problem......Page 206
Numerical solution of the Euler equations......Page 208
Finite volume schemes......Page 209
Evolution Galerkin methods......Page 210
Numerical experiments......Page 211
Discretization of the complete system of the Navier-Stokes equations......Page 212
Computational Results......Page 214
Introduction......Page 216
Review of some Results for Ordinary Differential Equations......Page 218
Solutions in D'_+......Page 219
Rough Statement of our Result......Page 220
Preliminaries......Page 221
Detailed Statement of our Result......Page 223
Sketch of the Proof of Theorem 14......Page 224
Mostafa......Page 228
Introduction......Page 234
Proof of Theorem A......Page 235
Proof of Theorem B......Page 236
A Conjecture......Page 240
Introduction......Page 242
Bounded Solutions......Page 243
L^p Solutions......Page 247
Introduction......Page 252
Preliminaries and result......Page 253
A priori estimates for the approximations......Page 256
A Nonlinear Model Problem......Page 260
Discretization......Page 261
A Posteriori Semidiscrete Error Indicators......Page 262
A Numerical Example......Page 264
Sklyar and Velkovsky......Page 268
 Introduction......Page 274
 Preliminaries......Page 276
Proof of Theorem 6......Page 277
 Introduction......Page 280
 Preliminaries......Page 281
 Properties of some integrals......Page 282
 Proof of Theorem 2......Page 283
Introduction and historical review......Page 286
Single beam equation......Page 289
"String-beam" system......Page 292
The first case - a single beam......Page 293
The second case - the coupling of a beam and a string......Page 297
The first case - a single beam......Page 300
The second case - the coupling of a beam and a string......Page 301
Final remarks and discussion......Page 303
The application of Banach contraction principle......Page 304
The general existence and uniqueness......Page 307
Introduction......Page 312
Virtual configurations and stresses......Page 313
Equations of type A......Page 315
Equations of type B......Page 318
Existence and convergence results......Page 319
Introduction......Page 324
Preliminaries......Page 326
Oscillation of equation (1)......Page 328
Oscillation of equation (2)......Page 329
Examples......Page 330
Author Index......Page 336
Subject Index......Page 338