Long-time behavior of second order evolution equations with nonlinear damping:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2008
|
| Series: | Memoirs of the American Mathematical Society
912 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 195, number 912 (third of 4 numbers)." Includes bibliographical references and index |
| Physical Description: | VIII, 183 S. |
| ISBN: | 9780821841877 |
Staff View
MARC
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| 245 | 1 | 0 | |a Long-time behavior of second order evolution equations with nonlinear damping |c Igor Chueshov ; Irena Lasiecka |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2008 | |
| 300 | |a VIII, 183 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 912 | |
| 500 | |a "Volume 195, number 912 (third of 4 numbers)." | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Attractors (Mathematics) | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Evolution equations, Nonlinear | |
| 650 | 4 | |a Attractors (Mathematics) | |
| 650 | 4 | |a Evolution equations, Nonlinear | |
| 650 | 4 | |a Differentiable dynamical systems | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface viii
Chapter
1.
Introduction
1
1.1.
Description of the problem studied
1
1.2.
The model and basic assumption
4
1.3.
Well-posedness
8
Chapter
2.
Abstract results on global attractors
17
2.1.
Criteria for asymptotic smoothness of dynamical systems
18
2.2.
Criteria for finite dimensionality of attractors
22
2.3.
Exponentially attracting positively invariant sets
28
2.4.
Gradient systems
32
Chapter
3.
Existence of compact global attractors for evolutions of the second
order in time
38
3.1.
Ultimate dissipativity
39
3.2.
Asymptotic smoothness: the main assumption
53
3.3.
Global attractors in
subcriticai case
56
3.4.
Global attractors in critical case
63
Chapter
4.
Properties of global attractors for evolutions of the second order
in time
90
4.1.
Finite dimensionality of attractors
90
4.2.
Regularity of elements from attractors
101
4.3.
Rate of stabilization to equilibria
113
4.4.
Determining functional
120
4.5.
Exponential fractal attractors
(inerţial
sets)
122
Chapter
5. Semilinear
wave equation with a nonlinear dissipation
125
5.1.
The model
125
5.2.
Main results
127
5.3.
Proofs
132
Chapter
6. Von
Karman
evolutions with a nonlinear dissipation
140
6.1.
The model
140
6.2.
Properties of
von
Karman
bracket
141
6.3.
Abstract setting of the model
142
6.4.
Model with rotational forces: a
> 0 144
6.5.
Non-rotational case a
= 0 152
Chapter
7.
Other models from continuum mechanics
158
vi
CONTENTS
7.1.
Berger s plate model
158
7.2.
Mindlin-Timoshenko plates and beams
164
7.3. Kirchhoff
limit in Mindlin-Timoshenko plates and beams
167
7.4.
Systems with strong damping
173
Bibliography
179
Index
183
|
| adam_txt |
Contents
Preface viii
Chapter
1.
Introduction
1
1.1.
Description of the problem studied
1
1.2.
The model and basic assumption
4
1.3.
Well-posedness
8
Chapter
2.
Abstract results on global attractors
17
2.1.
Criteria for asymptotic smoothness of dynamical systems
18
2.2.
Criteria for finite dimensionality of attractors
22
2.3.
Exponentially attracting positively invariant sets
28
2.4.
Gradient systems
32
Chapter
3.
Existence of compact global attractors for evolutions of the second
order in time
38
3.1.
Ultimate dissipativity
39
3.2.
Asymptotic smoothness: the main assumption
53
3.3.
Global attractors in
subcriticai case
56
3.4.
Global attractors in critical case
63
Chapter
4.
Properties of global attractors for evolutions of the second order
in time
90
4.1.
Finite dimensionality of attractors
90
4.2.
Regularity of elements from attractors
101
4.3.
Rate of stabilization to equilibria
113
4.4.
Determining functional
120
4.5.
Exponential fractal attractors
(inerţial
sets)
122
Chapter
5. Semilinear
wave equation with a nonlinear dissipation
125
5.1.
The model
125
5.2.
Main results
127
5.3.
Proofs
132
Chapter
6. Von
Karman
evolutions with a nonlinear dissipation
140
6.1.
The model
140
6.2.
Properties of
von
Karman
bracket
141
6.3.
Abstract setting of the model
142
6.4.
Model with rotational forces: a
> 0 144
6.5.
Non-rotational case a
= 0 152
Chapter
7.
Other models from continuum mechanics
158
vi
CONTENTS
7.1.
Berger's plate model
158
7.2.
Mindlin-Timoshenko plates and beams
164
7.3. Kirchhoff
limit in Mindlin-Timoshenko plates and beams
167
7.4.
Systems with strong damping
173
Bibliography
179
Index
183 |
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| discipline | Mathematik |
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| id | DE-604.BV035045722 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:54:45Z |
| indexdate | 2024-07-09T21:20:57Z |
| institution | BVB |
| isbn | 9780821841877 |
| language | English |
| lccn | 2008020750 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016714479 |
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| physical | VIII, 183 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Čuešov, Igor' D. 1951- Verfasser (DE-588)118042750 aut Long-time behavior of second order evolution equations with nonlinear damping Igor Chueshov ; Irena Lasiecka Providence, R.I. American Mathematical Society 2008 VIII, 183 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 912 "Volume 195, number 912 (third of 4 numbers)." Includes bibliographical references and index Attractors (Mathematics) Differentiable dynamical systems Evolution equations, Nonlinear Ordnung 2 (DE-588)4350619-7 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s Ordnung 2 (DE-588)4350619-7 s DE-604 Lasiecka, Irena 1948- Sonstige (DE-588)111374383 oth Memoirs of the American Mathematical Society 912 (DE-604)BV008000141 912 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016714479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Čuešov, Igor' D. 1951- Long-time behavior of second order evolution equations with nonlinear damping Memoirs of the American Mathematical Society Attractors (Mathematics) Differentiable dynamical systems Evolution equations, Nonlinear Ordnung 2 (DE-588)4350619-7 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4350619-7 (DE-588)4129061-6 |
| title | Long-time behavior of second order evolution equations with nonlinear damping |
| title_auth | Long-time behavior of second order evolution equations with nonlinear damping |
| title_exact_search | Long-time behavior of second order evolution equations with nonlinear damping |
| title_exact_search_txtP | Long-time behavior of second order evolution equations with nonlinear damping |
| title_full | Long-time behavior of second order evolution equations with nonlinear damping Igor Chueshov ; Irena Lasiecka |
| title_fullStr | Long-time behavior of second order evolution equations with nonlinear damping Igor Chueshov ; Irena Lasiecka |
| title_full_unstemmed | Long-time behavior of second order evolution equations with nonlinear damping Igor Chueshov ; Irena Lasiecka |
| title_short | Long-time behavior of second order evolution equations with nonlinear damping |
| title_sort | long time behavior of second order evolution equations with nonlinear damping |
| topic | Attractors (Mathematics) Differentiable dynamical systems Evolution equations, Nonlinear Ordnung 2 (DE-588)4350619-7 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Attractors (Mathematics) Differentiable dynamical systems Evolution equations, Nonlinear Ordnung 2 Evolutionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016714479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT cuesovigord longtimebehaviorofsecondorderevolutionequationswithnonlineardamping AT lasieckairena longtimebehaviorofsecondorderevolutionequationswithnonlineardamping |