Nonlinear parabolic-hyperbolic coupled systems and their attractors:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2008
|
| Series: | Operator theory
184 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 465 S. 235 mm x 165 mm |
| ISBN: | 9783764388140 9783764388133 3764388137 |
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MARC
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| 245 | 1 | 0 | |a Nonlinear parabolic-hyperbolic coupled systems and their attractors |c Yuming Qin |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a XV, 465 S. |c 235 mm x 165 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Operator theory |v 184 | |
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Record in the Search Index
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| adam_text |
Contents
Preface
Xl
1
Preliminary
1.1
Sobolev Spaces and Their Basic Properties
. 1
1.1.1
Distributions
. 2
1.1.2
Weak Derivatives and Sobolev Spaces
. 4
1.1.3
Sobolev Inequalities, Embedding Theorems
and the Trace Theorem
. 9
1.1.4
Interpolation Inequalities
. 17
1.1.5
The
Poincaré
Inequality
. 17
1.2
Some Inequalities in Analysis
. 18
1.2.1
The Classical Bellman-Gronwall Inequality
. 18
1.2.2
The Generalized Bellman-Gronwall Inequalities
. 19
1.2.3
The Uniform Bellman-Gronwall Inequality
. 20
1.2.4
The Nakao Inequalities
. 23
1.3
Some Differential Inequalities for Nonexistence of Global Solutions
. 25
1.4
Other Useful Inequalities
. 26
1.4.1
The Young Inequalities
. 27
1.4.2
The Holder Inequality
. 28
1.4.3
The Minkowski Inequalities
. 29
1.4.4
The Jensen Inequality
. 30
1.5
Co-Semigroups of Linear Operators
. 31
1.5.1
Co-Semigroups of Linear Operators
. 31
1.6
Global Attractors
. 37
1.6.1
Compact Semigroups (Semifiows) for Autonomous Systems
. 39
1.6.2
Weakly Compact Semigroups (Semiflows) for
Autonomous Systems
. 42
1.7
Bibliographic Comments
. 43
Contents
A One-dimensional Nonlinear Viscous and Heat-conductive Real Gas
2.1
Fixed and Thermally Insulated Boundary Conditions
. 46
2.1.1
Main Results
. 46
2.1.2
Uniform A Priori Estimates
. 49
2.2
Clamped and Constant Temperature Boundary Conditions
. 71
2.3
Exponential Stability in
Я
1 and
Я2
. 78
2.3.1
Main Results
. 78
2.3.2
Exponential Stability in
Я!
. 80
2.3.3
Exponential Stability in
Я2
. 89
2.4
Exponential Stability in
Я4
. 97
2.4.1
Global Existence in
Я4
. 100
2.4.2
A Nonlinear Co-Semigroup S(t) on
Я4
.
Ill
2.4.3
Exponential Stability in
Я4
. 119
2.5
Attractorsin
Я1 апаЯ2
. 123
2.5.1
An Absorbing Set in
Я1
. 126
2.5.2
An Absorbing Set in
Я2
. 132
2.6
Universal Attractor in
Я4
. 135
2.7
Bibliographic Comments
. 138
A One-dimensional Polytropic Viscous and Heat-conductive Gas
3.1
Initial Boundary Value Problems
.143
3.1.1
Global Existence and Asymptotic Behavior of Solutions
.143
3.1.2
Exponential Stability
.153
3.1.3
Universal Attractors
.154
3.2
The Cauchy Problem
.154
3.2.1
Global Existence in
Я2(Е)
.154
3.2.2
Large-Time Behavior of Solutions
.159
3.3
Bibliographic Comments
.164
A Polytropic Ideal Gas in Bounded Annular Domains in
Ж"
4.1
Global Existence and Asymptotic Behavior in
Я
'
and
Я2
.167
4.1.1
Uniform A Priori Estimates in
Я
x
.175
4.1.2
Uniform a priori estimates in
Я2
.187
4.1.3
Results in Eulerian Coordinates
.199
4.2
Exponential Stability in
Я4
.200
4.2.1
Main Results
.200
4.2.2
Global Existence in
Я4
.202
4.2.3
A Nonlinear Co-Semigroup
S(ř)
on
Я4
.211
4.2.4
Exponential Stability in
Я4
.222
4.3
Universal Attractors
.227
4.3.1
Nonlinear Semigroups on
Я2
.230
Contents ix
4.3.2
Existence
of an Absorbing
Set in
Яа(І)
. 231
4.3.3
Existence of an Absorbing Set in H^
. 236
4.3.4
Results of the Eulerian Coordinates
. 241
4.3.5
АйгасЮгіпЯ4
. 241
4.4
Bibliographic Comments
. 243
5
A Polytropic Viscous Gas with Cylinder Symmetry in M3
5.1
Main Results
. 245
5.2
Global Existence and Exponential Stability in
Я1
. 249
5.3
Global Existence and Exponential Stability in H2
. 266
5.4
Global Existence and Exponential Stability in
Я4
. 268
5.4.1
Global Existence of Solutions in
Я4
. 268
5.4.2
Exponential Stability in H%
. 285
5.5
Bibliographic Comments
. 290
6
One-dimensional Nonlinear Thermoviscoelasticity
6.1
Global Existence and Asymptotic Behavior of Solutions
. 293
6.2
Uniform A Priori Estimates
. 297
6.3
Exponential Stability and Maximal Attractors
. 325
6.4
Exponential Stability in
Я
'
and
Я2
. 331
6.5
Exponential Stability in
Я4
. 332
6.6
Universal Attractors in H' (i
= 1,2,4). 332
6.6.1
Existence of An Absorbing Set in
Яа'
. 332
6.6.2
Existence of An Absorbing Set in H$
. 335
6.6.3
Existence of An Absorbing Set in
Я4
. 336
6.7
Bibliographic Comments
. 336
7
A Nonlinear One-dimensional Thermoelastic System
with a Thermal Memory
7.1
Main Results
. 339
7.2
Global Existence and Exponential Stability
. 342
7.3
Bibliographic Comments
. 361
8
One-dimensional Thermoelastic Equations of Hyperbolic Type
8.1
Global Existence
. 363
8.2
Global Existence and Exponential Stability
. 365
8.3
Bibliographic Comments
. 379
χ
Contents
9
Blow-up for the Cauchy Problem in Nonlinear One-dimensional
Thermoelastìcity
9.1
Introduction
.381
9.2
Main Results
-
Case I
.382
9.3
Main Results
-
Case II
.399
9.4
Bibliographic Comments
.408
10
Large-Time Behavior of Energy in Multi-Dimensional Elasticity
10.1
Polynomial Decay of Energy
. 409
10.1.1
Main Results
. 411
10.1.2
Proof of Theorem
10.1.3. 413
10.2
Exponential Decay of Energy
. 421
10.2.1
Main Results
. 421
10.2.2
Proof of Theorem
10.2.3. 426
10.3
Bibliographic Comments
. 433
Bibliography
.435
Index
.463 |
| adam_txt |
Contents
Preface
Xl
1
Preliminary
1.1
Sobolev Spaces and Their Basic Properties
. 1
1.1.1
Distributions
. 2
1.1.2
Weak Derivatives and Sobolev Spaces
. 4
1.1.3
Sobolev Inequalities, Embedding Theorems
and the Trace Theorem
. 9
1.1.4
Interpolation Inequalities
. 17
1.1.5
The
Poincaré
Inequality
. 17
1.2
Some Inequalities in Analysis
. 18
1.2.1
The Classical Bellman-Gronwall Inequality
. 18
1.2.2
The Generalized Bellman-Gronwall Inequalities
. 19
1.2.3
The Uniform Bellman-Gronwall Inequality
. 20
1.2.4
The Nakao Inequalities
. 23
1.3
Some Differential Inequalities for Nonexistence of Global Solutions
. 25
1.4
Other Useful Inequalities
. 26
1.4.1
The Young Inequalities
. 27
1.4.2
The Holder Inequality
. 28
1.4.3
The Minkowski Inequalities
. 29
1.4.4
The Jensen Inequality
. 30
1.5
Co-Semigroups of Linear Operators
. 31
1.5.1
Co-Semigroups of Linear Operators
. 31
1.6
Global Attractors
. 37
1.6.1
Compact Semigroups (Semifiows) for Autonomous Systems
. 39
1.6.2
Weakly Compact Semigroups (Semiflows) for
Autonomous Systems
. 42
1.7
Bibliographic Comments
. 43
Contents
A One-dimensional Nonlinear Viscous and Heat-conductive Real Gas
2.1
Fixed and Thermally Insulated Boundary Conditions
. 46
2.1.1
Main Results
. 46
2.1.2
Uniform A Priori Estimates
. 49
2.2
Clamped and Constant Temperature Boundary Conditions
. 71
2.3
Exponential Stability in
Я
1 and
Я2
. 78
2.3.1
Main Results
. 78
2.3.2
Exponential Stability in
Я!
. 80
2.3.3
Exponential Stability in
Я2
. 89
2.4
Exponential Stability in
Я4
. 97
2.4.1
Global Existence in
Я4
. 100
2.4.2
A Nonlinear Co-Semigroup S(t) on
Я4
.
Ill
2.4.3
Exponential Stability in
Я4
. 119
2.5
Attractorsin
Я1 апаЯ2
. 123
2.5.1
An Absorbing Set in
Я1
. 126
2.5.2
An Absorbing Set in
Я2
. 132
2.6
Universal Attractor in
Я4
. 135
2.7
Bibliographic Comments
. 138
A One-dimensional Polytropic Viscous and Heat-conductive Gas
3.1
Initial Boundary Value Problems
.143
3.1.1
Global Existence and Asymptotic Behavior of Solutions
.143
3.1.2
Exponential Stability
.153
3.1.3
Universal Attractors
.154
3.2
The Cauchy Problem
.154
3.2.1
Global Existence in
Я2(Е)
.154
3.2.2
Large-Time Behavior of Solutions
.159
3.3
Bibliographic Comments
.164
A Polytropic Ideal Gas in Bounded Annular Domains in
Ж"
4.1
Global Existence and Asymptotic Behavior in
Я
'
and
Я2
.167
4.1.1
Uniform A Priori Estimates in
Я
x
.175
4.1.2
Uniform a priori estimates in
Я2
.187
4.1.3
Results in Eulerian Coordinates
.199
4.2
Exponential Stability in
Я4
.200
4.2.1
Main Results
.200
4.2.2
Global Existence in
Я4
.202
4.2.3
A Nonlinear Co-Semigroup
S(ř)
on
Я4
.211
4.2.4
Exponential Stability in
Я4
.222
4.3
Universal Attractors
.227
4.3.1
Nonlinear Semigroups on
Я2
.230
Contents ix
4.3.2
Existence
of an Absorbing
Set in
Яа(І)
. 231
4.3.3
Existence of an Absorbing Set in H^
. 236
4.3.4
Results of the Eulerian Coordinates
. 241
4.3.5
АйгасЮгіпЯ4
. 241
4.4
Bibliographic Comments
. 243
5
A Polytropic Viscous Gas with Cylinder Symmetry in M3
5.1
Main Results
. 245
5.2
Global Existence and Exponential Stability in
Я1
. 249
5.3
Global Existence and Exponential Stability in H2
. 266
5.4
Global Existence and Exponential Stability in
Я4
. 268
5.4.1
Global Existence of Solutions in
Я4
. 268
5.4.2
Exponential Stability in H%
. 285
5.5
Bibliographic Comments
. 290
6
One-dimensional Nonlinear Thermoviscoelasticity
6.1
Global Existence and Asymptotic Behavior of Solutions
. 293
6.2
Uniform A Priori Estimates
. 297
6.3
Exponential Stability and Maximal Attractors
. 325
6.4
Exponential Stability in
Я
'
and
Я2
. 331
6.5
Exponential Stability in
Я4
. 332
6.6
Universal Attractors in H' (i
= 1,2,4). 332
6.6.1
Existence of An Absorbing Set in
Яа'
. 332
6.6.2
Existence of An Absorbing Set in H$
. 335
6.6.3
Existence of An Absorbing Set in
Я4
. 336
6.7
Bibliographic Comments
. 336
7
A Nonlinear One-dimensional Thermoelastic System
with a Thermal Memory
7.1
Main Results
. 339
7.2
Global Existence and Exponential Stability
. 342
7.3
Bibliographic Comments
. 361
8
One-dimensional Thermoelastic Equations of Hyperbolic Type
8.1
Global Existence
. 363
8.2
Global Existence and Exponential Stability
. 365
8.3
Bibliographic Comments
. 379
χ
Contents
9
Blow-up for the Cauchy Problem in Nonlinear One-dimensional
Thermoelastìcity
9.1
Introduction
.381
9.2
Main Results
-
Case I
.382
9.3
Main Results
-
Case II
.399
9.4
Bibliographic Comments
.408
10
Large-Time Behavior of Energy in Multi-Dimensional Elasticity
10.1
Polynomial Decay of Energy
. 409
10.1.1
Main Results
. 411
10.1.2
Proof of Theorem
10.1.3. 413
10.2
Exponential Decay of Energy
. 421
10.2.1
Main Results
. 421
10.2.2
Proof of Theorem
10.2.3. 426
10.3
Bibliographic Comments
. 433
Bibliography
.435
Index
.463 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Qin, Yuming |
| author_GND | (DE-588)1119550041 |
| author_facet | Qin, Yuming |
| author_role | aut |
| author_sort | Qin, Yuming |
| author_variant | y q yq |
| building | Verbundindex |
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| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 SK 560 |
| ctrlnum | (OCoLC)228063664 (DE-599)DNB987617621 |
| 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 | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV035065030 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:01:59Z |
| indexdate | 2025-04-09T02:00:32Z |
| institution | BVB |
| isbn | 9783764388140 9783764388133 3764388137 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016733499 |
| oclc_num | 228063664 |
| open_access_boolean | |
| owner | DE-384 DE-824 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-384 DE-824 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 |
| physical | XV, 465 S. 235 mm x 165 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Qin, Yuming Verfasser (DE-588)1119550041 aut Nonlinear parabolic-hyperbolic coupled systems and their attractors Yuming Qin Basel [u.a.] Birkhäuser 2008 XV, 465 S. 235 mm x 165 mm txt rdacontent n rdamedia nc rdacarrier Operator theory 184 Differential equations, Nonlinear Differential equations, Partial System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf System von partiellen Differentialgleichungen (DE-588)4116672-3 s Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s DE-604 Operator theory 184 (DE-604)BV000000970 184 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016733499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Qin, Yuming Nonlinear parabolic-hyperbolic coupled systems and their attractors Operator theory Differential equations, Nonlinear Differential equations, Partial System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd |
| subject_GND | (DE-588)4116672-3 (DE-588)4221363-0 |
| title | Nonlinear parabolic-hyperbolic coupled systems and their attractors |
| title_auth | Nonlinear parabolic-hyperbolic coupled systems and their attractors |
| title_exact_search | Nonlinear parabolic-hyperbolic coupled systems and their attractors |
| title_exact_search_txtP | Nonlinear parabolic-hyperbolic coupled systems and their attractors |
| title_full | Nonlinear parabolic-hyperbolic coupled systems and their attractors Yuming Qin |
| title_fullStr | Nonlinear parabolic-hyperbolic coupled systems and their attractors Yuming Qin |
| title_full_unstemmed | Nonlinear parabolic-hyperbolic coupled systems and their attractors Yuming Qin |
| title_short | Nonlinear parabolic-hyperbolic coupled systems and their attractors |
| title_sort | nonlinear parabolic hyperbolic coupled systems and their attractors |
| topic | Differential equations, Nonlinear Differential equations, Partial System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd |
| topic_facet | Differential equations, Nonlinear Differential equations, Partial System von partiellen Differentialgleichungen Nichtlineare Evolutionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016733499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT qinyuming nonlinearparabolichyperboliccoupledsystemsandtheirattractors |