Dynamics of Evolutionary EquationsSpringer Science & Business Media, 2002. jan. 2. - 670 oldal The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations that attempt to model phenomena that change with time. The infi nite dimensional aspects occur when forces that describe the motion depend on spatial variables, or on the history of the motion. In the case of spatially depen dent problems, the model equations are generally partial differential equations, and problems that depend on the past give rise to differential-delay equations. Because the nonlinearities occurring in thse equations need not be small, one needs good dynamical theories to understand the longtime behavior of solutions. Our basic objective in writing this book is to prepare an entree for scholars who are beginning their journey into the world of dynamical systems, especially in infinite dimensional spaces. In order to accomplish this, we start with the key concepts of a semiflow and a flow. As is well known, the basic elements of dynamical systems, such as the theory of attractors and other invariant sets, have their origins here. |
Tartalomjegyzék
II | 1 |
III | 11 |
IV | 12 |
V | 15 |
VI | 16 |
VII | 19 |
VIII | 20 |
IX | 21 |
LXXXVII | 285 |
LXXXVIII | 293 |
LXXXIX | 299 |
XC | 313 |
XCI | 314 |
XCII | 318 |
XCIII | 319 |
XCIV | 321 |
X | 22 |
XI | 27 |
XII | 28 |
XIII | 29 |
XIV | 32 |
XV | 34 |
XVI | 35 |
XVII | 41 |
XVIII | 44 |
XIX | 45 |
XX | 48 |
XXI | 50 |
XXII | 53 |
XXIII | 61 |
XXIV | 62 |
XXV | 66 |
XXVI | 69 |
XXVIII | 73 |
XXIX | 76 |
XXX | 78 |
XXXI | 84 |
XXXII | 92 |
XXXIII | 103 |
XXXIV | 104 |
XXXV | 105 |
XXXVI | 111 |
XXXVII | 115 |
XXXVIII | 119 |
XXXIX | 120 |
XL | 126 |
XLI | 128 |
XLII | 137 |
XLIII | 141 |
XLIV | 143 |
XLV | 146 |
XLVI | 148 |
XLVII | 152 |
XLVIII | 161 |
XLIX | 171 |
L | 172 |
LI | 175 |
LII | 177 |
LIII | 185 |
LIV | 188 |
LV | 190 |
LVI | 192 |
LVII | 203 |
LVIII | 210 |
LIX | 216 |
LX | 221 |
LXI | 224 |
LXII | 225 |
LXIII | 228 |
LXIV | 229 |
LXV | 231 |
LXVI | 232 |
LXVII | 233 |
LXVIII | 234 |
LXIX | 235 |
LXX | 236 |
LXXI | 237 |
LXXII | 239 |
LXXIII | 244 |
LXXV | 246 |
LXXVI | 247 |
LXXVII | 249 |
LXXVIII | 251 |
LXXIX | 252 |
LXXX | 261 |
LXXXI | 267 |
LXXXII | 269 |
LXXXIV | 281 |
LXXXV | 283 |
LXXXVI | 284 |
XCV | 327 |
XCVI | 328 |
XCVII | 329 |
XCVIII | 335 |
XCIX | 339 |
C | 348 |
CI | 359 |
CII | 361 |
CIII | 362 |
CIV | 364 |
CV | 369 |
CVI | 373 |
CVII | 374 |
CVIII | 389 |
CIX | 395 |
CX | 396 |
CXI | 400 |
CXII | 401 |
CXIII | 403 |
CXIV | 406 |
CXV | 413 |
CXVI | 416 |
CXVIII | 419 |
CXIX | 424 |
CXX | 426 |
CXXI | 430 |
CXXII | 431 |
CXXIII | 433 |
CXXIV | 434 |
CXXV | 436 |
CXXVI | 442 |
CXXVII | 450 |
CXXVIII | 457 |
CXXIX | 460 |
CXXX | 464 |
CXXXI | 473 |
CXXXII | 481 |
CXXXIII | 483 |
CXXXIV | 488 |
CXXXV | 490 |
CXXXVI | 496 |
CXXXVII | 503 |
CXXXVIII | 505 |
CXXXIX | 513 |
CXL | 540 |
CXLI | 541 |
CXLII | 545 |
CXLIII | 548 |
CXLIV | 553 |
CXLVI | 554 |
CXLVII | 556 |
CXLVIII | 557 |
CXLIX | 560 |
CL | 562 |
CLI | 563 |
CLII | 565 |
CLIII | 569 |
CLIV | 570 |
CLV | 575 |
CLVI | 577 |
CLVII | 582 |
CLVIII | 589 |
CLIX | 591 |
CLX | 592 |
CLXI | 593 |
CLXII | 604 |
CLXIII | 613 |
CLXIV | 621 |
CLXV | 626 |
629 | |
655 | |
659 | |
Más kiadások - Összes megtekintése
Gyakori szavak és kifejezések
analytic semigroup assume asymptotically Banach space boundary conditions bounded set Bubnov-Galerkin classical solution Co-semigroup compact set constant convergence denote derivative dynamical systems e-At evolutionary equation exists exponential dichotomy Ətu finite following result Fréchet derivative Fréchet space function f Furthermore given global attractor Hale Hilbert space Hölder hyperbolic imbedding implies inertial manifold infinite dimensional integral interval invariant set Item K₁ L²(N Lemma linear operator linear skew product Lipschitz continuous longtime dynamics mapping maximally defined mild solution Navier-Stokes equations negative continuation nonempty nonlinear norm Note obtains partial differential equations perturbation positively invariant satisfies Section sectorial operator selfadjoint Sell semiflow S(t semigroup sequence skew product semiflow Sobolev spaces solution of equation Standing Hypothesis strong solution T(uo t₁ Temam term Theorem theory topology trichotomy u₁ unique valid weak solution
Hivatkozások erre a könyvre
Applications of Functional Analysis and Operator Theory V. Hutson,J. Pym,M. Cloud Korlátozott előnézet - 2005 |