New Trends in Mathematical Physics: In Honour of the Salvatore Rionero 70th Birthday Proceedings of the International Meeting Naples

Paolo Fergola, Florinda Capone, Maurizio Gentile, Gabriele Guerriero9789812560773, 98-1-256-077-7

This proceedings volume widely surveys new problems, methods and techniques in mathematical physics. The 22 original papers featured are of great interest to various areas of applied mathematics. They are presented in honour of the Professor Salvatore Rionero 70th birthday.

---

Table of contents :
CONTENTS……Page 10
Preface……Page 6
Conference Committee……Page 8
1 Introduction……Page 12
2 The mathematical model……Page 13
3 Time-discretization procedures……Page 17
4 Identification of the source……Page 20
References……Page 21
1 Introduction……Page 23
2 Notation and basic definitions……Page 25
3 Elliptic-parabolic tensors on Rn……Page 26
4 Commutation relations……Page 27
5 Elliptic metric tensors……Page 28
7 Elliptic-parabolic tensors as conformal Killing tensors……Page 31
References……Page 32
1 Considerazioni preliminari……Page 35
2 Le leggi costitutive. Le equazioni indefinite di equilibrio…….Page 36
3 Determinazione di un insieme di soluzioni delle equazioni di equilibrio e delle relative condizioni al contorno……Page 38
4 Genesi di una distorsione……Page 43
References……Page 44
1 Introduction……Page 45
2 The basic model……Page 46
3 Weak formulation……Page 50
4 An alternative model……Page 52
6 Conclusions……Page 54
References……Page 55
1 Introduction……Page 56
2 Steady, Unsteady, and Perturbation Problems…….Page 57
3 Analogous Estimate for a Steady Diffusion Problem in a Right Cylinder……Page 61
5 Appendix……Page 63
References……Page 64
1 The Cosmological Principle……Page 65
2 The Intrinsic Geometry of the Fluid u……Page 66
3 The Metrics for u in polar coordinates in Cases S3 and PS3……Page 67
4 Case E3 and Hubble’s Law……Page 68
5 On the Metrics of u in Cases E3, S3 and PS3……Page 69
6 The Intervention of the Velocity of Light……Page 71
7 The Velocity c and the Law of Composition for Velocities……Page 72
8 The Law of Composition for Velocities and the Hubble Sphere……Page 73
9 About Cosmography and the Deduction of the Function R(t)……Page 74
10 The Local Character of Special Relativity in Cosmology……Page 75
11 The Deduction of the Friedmann-Robertson-Walker Metric……Page 76
12 The Deduction of (7.1) in the Relativistic Context. The Minkowski Metric……Page 77
References……Page 78
1 Basic lexicon of classical statistical mechanics for spin systems……Page 79
2 Phase transitions……Page 81
3 Amorphous magnetic materials (spin glasses)……Page 82
4 Thermodynamic limit……Page 85
References……Page 87
2 Kinematical Premises……Page 88
3 Dynamics……Page 90
4 Gyroscopic Case……Page 91
References……Page 93
1 Introduction……Page 94
2 Equation P( ) + Q( )e- T = 0……Page 95
3 Equation P( ) + Q( )e -r + R( )e-2 r = 0……Page 96
4 Equation P(, r) + Q(, r)e-r = 0……Page 97
5 Equation P(, r ) + Q(, r)e-r + R(, r)e-2r = 0……Page 103
References……Page 105
1 Introduction……Page 106
2 Basic equations and linear Benard problem……Page 107
3 Critical Rayleigh curves……Page 109
4 Linear energy stability……Page 112
References……Page 116
1 Introduction……Page 118
2 Kinetic equations and their properties……Page 119
3.1 Approximation of the elastic terms……Page 123
3.2 Approximation of the inelastic terms……Page 124
4 The BGK-type model……Page 126
5 A numerical test……Page 127
References……Page 131
1 Introduction……Page 132
2 The stability problem……Page 133
3 Nonlinear stability results in the BQnard problems: Rionero’s contributions and some new results……Page 135
References……Page 141
2 Preliminaries……Page 143
3 Multilattice kinematics……Page 144
4 Phase changes in a wt-nbhd……Page 148
5 The case of -quartz……Page 151
References……Page 156
1 Introduction……Page 158
2.1 Standard Doctrine……Page 159
2.2 Contact Power, Distance Power, and Contact Flux……Page 160
3.1 Grade-I Elasticity……Page 161
3.2 Grade-2 Elasticity……Page 162
4 Contact Flux and Stress(es) Associated with Null Lagrangians……Page 163
4.1 Grade-1 Null Lagrangaans……Page 164
4.2 Grade-2 Null Lagrangians……Page 165
References……Page 167
1 Introduction……Page 168
2 Mass conservation……Page 169
3.1 Production and destruction……Page 172
3.2 Mass fluxes……Page 174
4.1 Momentum balance……Page 175
4.2 Specific assumptions……Page 176
5 A different approach……Page 177
5.2 Chemical potential……Page 178
5.3 A numerical simulation……Page 180
References……Page 181
1 Introduction……Page 183
2 Equations of Motion……Page 184
2.1 Flow between two plates rotating about non-coincident axes…….Page 185
2.2 Torsional Flow……Page 190
References……Page 194
1 Introduction……Page 195
2 Basic properties of the fundamental solution……Page 196
3 Linear evolution and explicit behavior……Page 198
4 Estimates for non linear problems……Page 201
References……Page 202
1 Structural model……Page 204
3 Bilateral constraints……Page 208
4 Korn’s inequality……Page 210
5 Basic theorems……Page 211
6 Boundary value problems……Page 212
References……Page 215
1 Introduction……Page 216
2.2 The Kawashima condition……Page 217
2.4 Kawashima Condition for the mixture……Page 218
4 Shock Waves……Page 220
4.1 Sonic Shock……Page 221
4.2 Diffusive Shock……Page 222
4.3 Characteristic Shock……Page 223
References……Page 224
1 Introduction……Page 226
3 Energy stability and porous convection……Page 227
References……Page 228
1 Introduction and the Model……Page 230
2 Differentiation among species by carrying capacity……Page 232
3 Differentiation among species by carrying capacity and intrinsic growth rate……Page 235
4 Conclusions……Page 243
References……Page 244
1 Introduction……Page 245
2 Extremal distributions and Wasserstein-type metrics……Page 246
3 Porous medium equations……Page 248
4 Nonlinear friction equations……Page 250
5 Nonlinear friction equations with viscosity……Page 252
6 Degenerate convection-diffusion equations……Page 253
Acknowledgments……Page 254
References……Page 255
Opening Talks……Page 256
Acknowledgements……Page 274