Attractors of evolution equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Amsterdam u.a.
North-Holland
1992
|
| Schriftenreihe: | Studies in mathematics and its applications
25 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | X, 532 S. |
| ISBN: | 0444890041 |
Internformat
MARC
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| 100 | 1 | |a Babin, Anatolij V. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Attraktory evoljucionnych uravnenij |
| 245 | 1 | 0 | |a Attractors of evolution equations |c A. V. Babin and M. I. Vishik |
| 264 | 1 | |a Amsterdam u.a. |b North-Holland |c 1992 | |
| 300 | |a X, 532 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Studies in mathematics and its applications |v 25 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 4 | |a Attracteur | |
| 650 | 4 | |a Dimension Hausdorff | |
| 650 | 4 | |a Ensemble invariant | |
| 650 | 4 | |a Equation Navier-Stokes | |
| 650 | 4 | |a Equation évolution | |
| 650 | 4 | |a Navier-Stokes, Équations de - Solutions numériques | |
| 650 | 7 | |a Navier-Stokes, équations - Solutions numériques |2 ram | |
| 650 | 4 | |a Semi-groupe opérateur | |
| 650 | 4 | |a Système dynamique | |
| 650 | 4 | |a Attractors (Mathematics) | |
| 650 | 4 | |a Navier-Stokes equations |x Numerical solutions | |
| 650 | 0 | 7 | |a Attraktor |0 (DE-588)4140563-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Evolutionsgleichung |0 (DE-588)4129061-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Navier-Stokes-Gleichung |0 (DE-588)4041456-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
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| 689 | 1 | 0 | |a Evolutionsgleichung |0 (DE-588)4129061-6 |D s |
| 689 | 1 | 1 | |a Attraktor |0 (DE-588)4140563-8 |D s |
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Datensatz im Suchindex
| _version_ | 1804119296583925760 |
|---|---|
| adam_text | vii
CONTENTS
PREFACE V
INTRODUCTION 1
Chapter 1
QUASILINEAR EVOLUTIONARY EQUATIONS AND SEMIGROUPS
GENERATED BY THEM 13
1. Functional spaces and embedding theorems 13
2. Operator semigroups. Basic notions 29
3. Semigroup generated by a parabolic equation
with a monotone principal part 34
4. Properties of the semigroup of Section 3 47
5. Semigroups generated by reaction diffusion
systems 63
6. Two dimensional Navier Stokes system 76
7. Quasilinear equations and semigroups in C ^(n)
and in VTCr ) 90
p
8. Damped hyperbolic equation 103
Chapter 2
MAXIMAL ATTRACTORS OF SEMIGROUPS 117
1. Attracting sets (general concepts) 117
2. Theorems on existence of maximal attractors 121
3. Attractors of parabolic equations with a monotone
principal part 127
4. Attractor of the two dimensional Navier Stokes
system 129
5. Attractors of semigroups in C (n) and in W (t ) 130
p
6. Attractor of the hyperbolic equation 131
7. On the behaviour of trajectories as time tends to
minus infinity 146
8. Injectivity of operators of semigroups 148
Chapter 3
ATTRACTORS AND UNSTABLE SETS 157
1. Unstable and stable sets 157
2. Global Lyapunov function and the structure of an
viii Contents
invariant set 159
3. Examples of evolutionary equations having a global
Lyapunov function 163
4. Investigation of the attractor of a hyperbolic
equation using the dissipation integrals 171
5. Evolutionary equations with the convergent
dissipation integral 176
6. Applications to monotone parabolic equations 181
7. Decomposition of an attractor into the union of
rest tending and rest untending components 184
8. Examples of semigroups whose attractors may be
decomposed into rest tending and rest untending
components 188
Chapter 4
SOME INFORMATION ON SEMIGROUPS OF LINEAR OPERATORS 193
1. Semigroups of linear operators with a basis
of eigenvectors 193
2. Almost stable operator semigroups 201
3. Examples of almost stable semigroups generated by
parabolic equations 206
4. On almost stability of semigroups corresponding
to equations which are not parabolic 209
Chapter 5
INVARIANT MANIFOLDS OF SEMIGROUPS AND MAPPINGS AT
EQUILIBRIUM POINTS 217
1. Local unstable sets and local attraction 217
2. Invariant manifold of a mapping which is close
to linear 221
3. Invariant manifold in a neighbourhood of a
hyperbolic equilibrium point 240
4. Spectral asymptotics as time tends to infinity for
trajectories tending to an equilibrium point 248
5. Theorems on linearization 260
6. Regular attractors 270
7. Uniform spectral asymptotics as t » » of
trajectories of semigroups having a Lyapunov
function 279
Chapter 6
STEADY STATE SOLUTIONS 297
1. Compactness of the set of steady state solutions 297
2. The Sard Smale theorem 301
3. Examples of applications of the Sard Smale theorem 308
4. Lower bounds for the instability index of
equilibrium points 318
5. Lower bound for the instability index of
Contents ix
steady state solutions of the two dimensional
Navier Stokes system 330
6. On the variation of the index of instability on
stationary curves 335
Chapter 7
DIFFERENTIABILITY OF OPERATORS OF SEMIGROUPS
GENERATED BY PARTIAL DIFFERENTIAL EQUATIONS 341
1. Differentiability of operators of a semigroup
corresponding to an evolution equation 341
2. Extension of a semigroup from a neigbourhood of an
equilibrium point to a semigroup defined on the
whole space 351
3. Differentiability of operators of a semigroup
corresponding to a parabolic system 368
4. Differentiability of the semigroup corresponding
to a damped hyperbolic equation 378
5. Differentiability of operators of the semigroup
corresponding to the two dimensional Navier Stokes
system 383
6. Differentiability of the operators S acting in
2+£t
the space C in the case of a parabolic
equation 386
7. The three dimensional Navier Stokes system in a
neighbourhood of an equilibrium point 392
Chapter 8
SEMIGROUPS DEPENDING ON A PARAMETER 399
1. Semigroups of operators depending on a parameter
and the Lyapunov stability modulo attractor 399
2. The case of exponential rate of attraction to the
attractor 405
3. Continuous dependence of unstable manifolds
on a parameter 408
4. Examples of attractors upper semicontinuously
depending on a parameter 410
5. Attractors of singularly perturbed
evolutionary equations 416
Chapter 9
DEPENDENCE ON A PARAMETER OF ATTRACTORS
OF DIFFERENTIABLE SEMIGROUPS AND UNIFORM
ASYMPTOTICS OF TRAJECTORIES 423
1. Dependence of regular attractors on a parameter 423
2. Uniformly in time stabilized principal term of
asymptotics of semigroups depending on a parameter 434
3. Examples of equations regularly depending on a
parameter 452
x Contents
4. Uniformly with respect to time stabilized
principal term of asymptotics of solutions of
singularly perturbed equations 465
Chapter 10
HAUSDORFF DIMENSION OF ATTRACTORS 479
1. Hausdorff dimension of invariant sets 479
2. A bound for the Hausdorff dimension of
the attractor of a reaction diffusion system 487
3. Estimate of the Hausdorff dimension of the
attractor of the two dimensional Navier StoJces
system 492
4. Estimates of dimension of regular attractors 498
5. Some systems of mathematical physics which have
finite dimensional attractors 502
BIBLIOGRAPHY 505
INDEX 527
|
| any_adam_object | 1 |
| author | Babin, Anatolij V. Višik, Marko I. 1921-2012 |
| author_GND | (DE-588)129619701 |
| author_facet | Babin, Anatolij V. Višik, Marko I. 1921-2012 |
| author_role | aut aut |
| author_sort | Babin, Anatolij V. |
| author_variant | a v b av avb m i v mi miv |
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| classification_tum | MAT 354f MAT 587f |
| ctrlnum | (OCoLC)25131098 (DE-599)BVBBV005153253 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005153253 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:23:56Z |
| institution | BVB |
| isbn | 0444890041 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003177124 |
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| physical | X, 532 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | North-Holland |
| record_format | marc |
| series | Studies in mathematics and its applications |
| series2 | Studies in mathematics and its applications |
| spelling | Babin, Anatolij V. Verfasser aut Attraktory evoljucionnych uravnenij Attractors of evolution equations A. V. Babin and M. I. Vishik Amsterdam u.a. North-Holland 1992 X, 532 S. txt rdacontent n rdamedia nc rdacarrier Studies in mathematics and its applications 25 Aus d. Russ. übers. Attracteur Dimension Hausdorff Ensemble invariant Equation Navier-Stokes Equation évolution Navier-Stokes, Équations de - Solutions numériques Navier-Stokes, équations - Solutions numériques ram Semi-groupe opérateur Système dynamique Attractors (Mathematics) Navier-Stokes equations Numerical solutions Attraktor (DE-588)4140563-8 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Evolutionsgleichung (DE-588)4129061-6 s Attraktor (DE-588)4140563-8 s Višik, Marko I. 1921-2012 Verfasser (DE-588)129619701 aut Studies in mathematics and its applications 25 (DE-604)BV000000646 25 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003177124&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Babin, Anatolij V. Višik, Marko I. 1921-2012 Attractors of evolution equations Studies in mathematics and its applications Attracteur Dimension Hausdorff Ensemble invariant Equation Navier-Stokes Equation évolution Navier-Stokes, Équations de - Solutions numériques Navier-Stokes, équations - Solutions numériques ram Semi-groupe opérateur Système dynamique Attractors (Mathematics) Navier-Stokes equations Numerical solutions Attraktor (DE-588)4140563-8 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4140563-8 (DE-588)4129061-6 (DE-588)4041456-5 (DE-588)4128130-5 |
| title | Attractors of evolution equations |
| title_alt | Attraktory evoljucionnych uravnenij |
| title_auth | Attractors of evolution equations |
| title_exact_search | Attractors of evolution equations |
| title_full | Attractors of evolution equations A. V. Babin and M. I. Vishik |
| title_fullStr | Attractors of evolution equations A. V. Babin and M. I. Vishik |
| title_full_unstemmed | Attractors of evolution equations A. V. Babin and M. I. Vishik |
| title_short | Attractors of evolution equations |
| title_sort | attractors of evolution equations |
| topic | Attracteur Dimension Hausdorff Ensemble invariant Equation Navier-Stokes Equation évolution Navier-Stokes, Équations de - Solutions numériques Navier-Stokes, équations - Solutions numériques ram Semi-groupe opérateur Système dynamique Attractors (Mathematics) Navier-Stokes equations Numerical solutions Attraktor (DE-588)4140563-8 gnd Evolutionsgleichung (DE-588)4129061-6 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Attracteur Dimension Hausdorff Ensemble invariant Equation Navier-Stokes Equation évolution Navier-Stokes, Équations de - Solutions numériques Navier-Stokes, équations - Solutions numériques Semi-groupe opérateur Système dynamique Attractors (Mathematics) Navier-Stokes equations Numerical solutions Attraktor Evolutionsgleichung Navier-Stokes-Gleichung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003177124&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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