|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Garbey M., Kaper H.G. — Asymptotic Analysis and the Numerical Solution of Partial Differential Equations, Vol. 130 |
|
|
|
| Предметный указатель |
Accelerating wave 162
Acoustic stability 178
Activation energy 254 256
Aerodynamics, transonic 145
Algebraic manipulation software 241
Analysis, synergism with computation 50
Arrhenius kinetics 162
Asymptotic analysis, domain decomposition methods with 39
Asymptotic analysis, multiple scales problems 77
Asymptotic analysis, singular-perturbation problems 33
Asymptotic approximation 11
Asymptotic boundary conditions 106 109
Asymptotic evaluation of integrals 11
Asymptotic expansion 39 57 58
Asymptotic theory, verification 178
Asymptotically induced domain decomposition 59—77
Asymptotics, diffusion equations 246
Asymptotics, far fields 99 104
Asymptotics, matched 53
Atmospheric approximation 141
Axisymmetric bodies 155
Basin of attraction, boundaries of 26
Bifurcation analysis, with MAPLE 254 258 262
Bifurcation diagrams 261
Bifurcation parameter 257
Bifurcations, vertical 261
Blow-up of solutions of nonlinear heat and wave equations 217
Blow-up points 218
Blow-up time 220
Blow-up, survey article on 219
Boundary conditions, asymptotic 106 109
Boundary conditions, radiation 99
Boundary functions, continuous conditions for 59
Boundary layer problems, elliptic 55
Boundary layer problems, parabolic 56
Boundary layers and multiple scale problems 75
Boundary layers, birth of 39
Boundary layers, interior layer interactions with 14
Boundary layers, ordinary 38
Boundary layers, parabolic 39
Boundary value problems, applications 6 11
Boundary value problems, free 253
Boundary value problems, initial 109 140
Boundary value problems, limiting solutions 5 7 9—11 13
Boundary value problems, positive solutions of 246
Boundary value problems, radial solutions of 246
Boundary value problems, spectral decomposition of solution 37
Boundary value problems, two-point 3 11
Boundary, burnt 111
Bubnov — Galerkin approximation 115 116
Burgers' equation 11 79 176 226 227
Capture of oscillations 26 29
Cauchy problem 219 221 222
Cellular automata 196
Cellular detonation 175 180
Cellular fluids 196
Changing variables, with MAPLE 249
Chaos, molecular 198
Chapman — Enskog analysis 196 202
Chapman — Jouguet velocity 173
Chin — Krasny method 44 45
Choked transonic flow 155
Combustion, bifurcation phenomena, with MAPLE 254
Combustion, condensed phase 254
Combustion, mathematical model 255
Combustion, modeling 108
Combustion, multiple point 255 259
Combustion, nonlinear hyperbolic equation in 222
Combustion, propagation of front 255
Combustion, pulsating waves 259
Combustion, spin 255
Combustion, spinning waves 259
Combustion, standing waves 259
Combustion, theory 223
Combustion, traveling waves 259
Combustion, uniformly propagating plane front 256
Comparison techniques, with MAPLE 250
Connection formulas 17 18 30—31
Conservation laws, classical solution 225
Conservation laws, convergence to steady state 225
Conservation laws, eigensolutions 226 236
Conservation laws, lattice methods 201
Conservation laws, scalar 81
Conservation laws, steady-state solutions 225
Conservation laws, weak solutions 225
Convection-diffusion equation, singularly perturbed 35
Convection-reaction-diffusion equation 45
Coriolis force 137 142
Cylindrical domains 100
Decomposition, global 42
Decomposition, spectral 37
Deflagration 161
Detonation shock dynamics (DSD) 178
Detonation, accelerating subsonic reaction wave with 162
Detonation, applications 178
Detonation, cellular 173
Detonation, cellular wave structure 178
Detonation, CJ velocity 173
Detonation, conventional 162
Detonation, high-speed 159
Detonation, mathematical model 171
Detonation, multidimensional 172
Detonation, near-CJ 173
Detonation, one dimensional 171
Detonation, precursor shock 162
Detonation, reaction zone 171
Detonation, shock and reaction zone 169
Detonation, shock waves 171
Detonation, verification of asymptotic theory 178
Detonation, weak 162
Detonation, weakly curved shock 174
Detonation, ZND model 171
Differential geometry 40
Diffusion equation, semilinear, asymptotics of solutions 246
Diffusion equation, semilinear, boundary value problems 246
Diffusion equation, semilinear, critical exponent 246 249
Diffusion equation, semilinear, Dirichlet problem 247
Diffusion equation, semilinear, existence of solutions 246
Diffusion equation, semilinear, free boundary problem 253
Diffusion equation, semilinear, ground state solution 248
Diffusion equation, semilinear, open problems 249
Diffusion equation, semilinear, positive solutions 246
Diffusion equation, semilinear, radial solutions 246 249
Diffusion equation, semilinear, Sobolev exponent 247 249
Diffusion equation, semilinear, subcritical exponent 247
Diffusion equation, semilinear, supercritical exponent 247
Diffusion equation, semilinear, uniqueness of solutions 246 250 251—253
Dirichlet problem, domain decomposition methods with 32
Dirichlet problem, semilinear diffusion equations with 247
dispersion relation 257
Dissipative perturbations and amplitude of oscillations 17
Dissipative perturbations, illustration 20
Disturbance theory 130
Domain decomposition for convection-diffusion problems 35
Domain decomposition for multiple scales problems 34
Domain decomposition for parabolic boundary layer problems 60
Domain decomposition in parallel computation 32
Domain decomposition method 249
Domain decomposition, asymptotic structure of solution used with 39
Domain decomposition, asymptotically induced 55
Domain decomposition, boundary-fitting charts needed with 52
Domain decomposition, convergence 66
Domain decomposition, divergence 68
Domain decomposition, heterogeneous 137
Domain decomposition, history 33
Domain decomposition, hybrid-perturbation Galerkin method with 130
Domain decomposition, orthogonal polynomials generated with 47
Domain decomposition, spectral 37
Double-well potentials 19
Drag in not-so-slender bodies 149
| Drag, effect of Mach number 145
Drag, transonic coordinates 146
Dynamical system 259 262
Eigensolutions to conservation laws 226 236
Eigenvalue problem 100 225 226 228 231 234
Elliptic boundary layer problems 55
Emden-Fowler equation 247 249
Energy considerations, Melnikov type 24 26—28
Energy dissipation 24
Energy, activation 254 256
Entropy condition, geometric 81
Euler equations 171
Evolution equations 175
Exchange of stability 262
Explosion 161
Extinction 109
Far fields as perturbations of sonic flow 153
Far fields in near-sonic flows 252
Far fields, asymptotics 99 104
Fast/slow system 5
Fermi Exclusion Principle 199
Finite difference methods, comparison with lattice Boltzmann methods 204
Finite difference methods, conditionally monotone 196
Finite difference methods, relationship to lattice gas methods 198
Flame propagation 100 108
Forward marching 48 50
Free boundary problem 254
Galerkin method, combined with perturbation techniques 113
Gasdynamic equations, detonation 171
Gasdynamic equations, interaction of shock and rarefaction 92
Gasdynamic equations, nozzle flow 229—236
Gasdynamic equations, simple shock 91
Geometric entropy condition 79
Geometry, differential 40
Geometry, phase-plane 3 12 13
Geostrophic initialization 143
Geostrophy, equations 142
Global decomposition 42
Godunov method 83 86 87 91
Group velocity 101
Heat equations, hyperbolic 222
Heat equations, nonlinear 217
Heterogeneous domain decomposition 137
Heterojunction devices, away from the solution 190
Heterojunction devices, bandgaps 186
Heterojunction devices, inner solution 188
Heterojunction devices, materials in 186
Heterojunction devices, outer solution 187
Heterojunction devices, simulation of 186
Homoclinic orbit 18
Hybrid perturbation-Galerkin method with domain decomposition 130
Hybrid perturbation-Galerkin method, application to problem involving compressible flow 122
Hybrid perturbation-Galerkin method, description 115
Hybrid perturbation-Galerkin method, example 117
Hybrid perturbation-Galerkin method, semi-analytical technique 128
Hybrid perturbation-Galerkin method, semi-numerical technique 128
Hybrid perturbation-Galerkin method, summary 114
Hyperbolic equations, in combustion 222
Induction equations 165
Induction flame 168 169 171
Induction Period 164
Induction time, constant-pressure 163 165
Initial boundary value problems for solving propagating flames problems 109
Initial boundary value problems in ocean modeling 140
Integrals, asymptotic evaluation of 60 62
Integrals, asymptotic expansion of 3 11
Kolodner — Coffman method 250
Laplace's method 101 102
Lattice Boltzmann methods, Chapman — Enskog analysis 202
Lattice Boltzmann methods, comparison with finite difference methods 203
Lattice Boltzmann methods, equations 201
Lattice Boltzmann methods, origin from lattice gas methods 198
Lattice gas automata 196
Lattice gas methods for fluid dynamics models 197
Lattice gas methods, collision operator 200
Lattice gas methods, collision rules 20
Lattice gas methods, conservation laws with 201
Lattice gas methods, microdynamical equation 199
Lattice gas methods, occupation number 199
Lattice gas methods, state transition function 200
Leading-order energy, definition 20
Leading-order energy, dissipation of 23
Leading-order energy, time evolution of 21
Lienard equation 3 8
Lienard plane 5 7 8
Lienard variable 5
Linear function, in boundary layer 48
Lyapunov functions 250
Macsyma 241
Maple 241—264
MAPLE, bifurcation analysis 254 258 262
MAPLE, changing variables with 249
MAPLE, comparison techniques with 250
MAPLE, introduction to 242—246
MAPLE, series solutions generated with 247
MAPLE, study of bifurcation phenomena in combustion 254
MAPLE, verifying conditions with 253
Marching, forward 50 52
Matching to transition region 28
Matching with asymptotic expansions 41 51 76 79 84
Mathematica 241
Mean occupation numbers 199
Melnikov-type energy considerations 24—26
Melting parameter 256
Microdynamical equation 197
Minimum viscosity method 84 89
Modeling, combustion 108 255
Modeling, detonation 173
Modeling, ocean 139—140 143
Molecular chaos 198
Monotonicity, conditions of 200
Multiple point combustion 255
Multiple scales method 20
Multiple scales problems, accuracy improved with asymptotic analysis 75
Multiple scales problems, domain decomposition methods with 34
Multiple scales problems, ocean models 139
Multiple scales problems, variation with 34
Navier — Stokes equations 100 102 107 198
Neutral stability curve 258
Not-so-slender bodies 148 149
Nozzle flow, gasdynamic equations 226
Nozzle flow, inviscid case 229 231
Nozzle flow, viscous case 230
Numerical computation, comparison with matched asymptotics 53
Occupation number 199
Ocean modeling 139—140 143
Orthogonal polynomials 47
Oscillation of second-order equations 250
Oscillation, capture of 25 29
Parabolic boundary layer problems 59
Parabolic equations, higher order 219
Parabolic layers 59 62 63 77
Parallel computation, with domain decomposition 33
Perturbation techniques for solutions to PDEs 114
Perturbation techniques for sonic flow problems 151
Perturbation techniques with Galerkin method 113
Perturbation techniques, dissipative 17 19
Perturbations, singular 3—16
Phase condition 110
Phase front 256 259
Phase-plane geometry 3 12 13
Planar traveling waves 109
Polynomials, orthogonal 47
Preuss's method 43 45
Propagation of combustion front 255
Propagation, theory 100
Pulsating waves 259
Pulses, solitary 26 27
Quantum Liouville equation for large heterojunction devices 186
Quantum Liouville equation for small analog devices 186
|
|
|
| Реклама |
|
|
|
|
|
О проекте