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| Henry D. — Geometric Theory of Semilinear Parabolic Equations |
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| Предметный указатель |
 -bounds 74
Analytic semigroup, definition of 20
Analytic semigroup, generator of 20
Analyticity 11
Asymptotically autonomous 96
Averaging 66 68 69 221 292—294
Bifurcation, from a focus 181—187
Bifurcation, of equilibria 178 263
Bifurcation, to a circle in diffeomorphisms 266—274
Bifurcation, to a torus 266—274
Bifurcation, transfer of stability at 178—263
Burger's equation 134—135
Center manifold, approximation of 171
Center manifold, existence and stability 168
Center-stable manifold 116
Center-unstable manifold 262
Channel flow, swelling of 117
Characteristic multiplier 197
Chemical reactions 43 82 167
Combustion theory 101 158 319—330
Contraction principle 12 13
Dichotomies, exponential, definition of 224
Dichotomies, exponential, discrete 229
Dichotomies, exponential, implications of 227
Dichotomies, exponential, perturbation of 237 238 240 242 245
Dynamical system 82
Embedding theorems 9 35—40
Equilibrium point 83
Essential spectrum, characterization of 140
Essential spectrum, definition of 136
Essential spectrum, examples of 140—142
Fractional powers, definition of 24
Fractional powers, examples of 32—40
Frechet derivative 10
Gradient flow, an example of 118—128
Gradient flow, domains of attraction in 123—125
Gradient flow, maximal invariant set of 126—127
Heat equation 16 41
Hodgekin — Huxley equation 42
Implicit function theorem 15
Instability, criterion for 102 104 105 107 109
Integral inequalities 188—190
Invariance principle 92 93
Invariant manifold, coordinate system near some 304
Invariant manifold, definition of 143 154
Invariant manifold, existence of 143 161 164 165 275 297
Invariant manifold, extensions of local 154 156
Invariant manifold, further properties of 289—291
Invariant manifold, smoothness of 152 278
Invariant manifold, stability of 147 150 277 297
Invariant set 91
Liapunov function 84
Maximum principle 60 61 109
Navier — Stokes equation 45 79
Nirenberg — Gagliardo inequalities 37
| Nonautonomous linear equations 190
Nonautonomous linear equations, adjoint of 204
Nonautonomous linear equations, backward uniqueness 208 209
Nonautonomous linear equations, density of range of solution operator of 207
Nonautonomous linear equations, estimates on solution of 191
Nonautonomous linear equations, nonhomogeneous 193
Nonautonomous linear equations, periodic 197
Nonautonomous linear equations, slowly varying coefficients of 213
Nuclear reactors 44 62 95
Omega limit set 91
Operator, fractional powers of 24 25
Operator, products of 28
Operator, sectorial 18
Operator, spectral set of 30
Operator, sums of 19 27
Periodic linear systems 197
Periodic linear systems, Floquet theory of 198
Periodic linear systems, Fredholm alternative for 206
Periodic linear systems, stability of 200
Periodic orbit 83
Periodic orbit, coordinate system near 299
Periodic orbit, families of 309
Periodic orbit, instability of 254
Periodic orbit, perturbation of 256 257
Periodic orbit, stability of 251
Periodic solutions, instability of 249
Periodic solutions, perturbation of 255
Periodic solutions, stability of 247
Poincare map 258—261
Population genetics 43 314—319
Predator-prey systems 201 312
Saddle-point property 112
Sectorial operator, definition of 18
Sectorial operator, fractional powers of 24 25
Sectorial operator, properties of 19 23
Semiconductors 42
Solution of differential equation, classical 75—76
Solution of differential equation, compactness of 57
Solution of differential equation, continuation of 55
Solution of differential equation, continuous dependence of 62
Solution of differential equation, definition of 53
Solution of differential equation, differentiability of 64 71 72
Solution of differential equation, existence of 54 59
Solution of differential equation, uniqueness of 54 59
Spaces  , definition of 29
Spaces , properties of 29
Spectral set 30
Stability, converse theorem of 86 90
Stability, criteria for 84 98 100
Stability, definitions of 83
Stability, invariance principle for 92 93
Stability, of families 108
Stability, orbital 84
Stability, under constant disturbances 88 90
Traveling waves, existence 129
Traveling waves, stability of 130—133
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