Transport equations and multi-D hyperbolic conservation laws:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer [u.a.]
2008
|
| Series: | Lecture notes of the Unione Matematica Italiana
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIV, 130 S. graph. Darst. 24 cm |
| ISBN: | 9783540767800 3540767800 |
Staff View
MARC
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| 245 | 1 | 0 | |a Transport equations and multi-D hyperbolic conservation laws |c Luigi Ambrosio ... Ed. Fabio Ancona ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer [u.a.] |c 2008 | |
| 300 | |a XIV, 130 S. |b graph. Darst. |c 24 cm | ||
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| 490 | 1 | |a Lecture notes of the Unione Matematica Italiana |v 5 | |
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Record in the Search Index
| _version_ | 1804137718646571008 |
|---|---|
| adam_text | Contents
Parti
Existence, Uniqueness, Stability and Differentiability Properties
of the Flow Associated to Weakly Differentiable Vector Fields
.......... 3
Luigi Ambrosio
and Gianluca Crippa
1
Introduction
.................................................... 3
2
The Continuity Equation
......................................... 5
3
The Continuity Equation Within the Cauchy-Lipschitz Framework
...... 7
4
(ODE) Uniqueness Vs. (PDE) Uniqueness
.......................... 11
5
The Flow Associated to Sobolev or
B V
Vector Fields
................. 19
6
Measure-Theoretic Differentials
................................... 32
7
Differentiability of the Flow in the W1 1 Case
........................ 38
8
Differentiability and Compactness of the Flow in the W1 ? Case
........ 40
9
Bibliographical Notes and Open Problems
.......................... 52
References
........................................................ 54
Part
Π
A Note on Alberti s Rank-One Theorem
............................ 61
Camfflo
De Leilis
1
Introduction
.................................................... 61
2
Dimensional Reduction
.......................................... 63
3
A Blow-Up Argument Leading to a Partial Result
.................... 65
4
The Fundamental Lemma
........................................ 66
5
Proof of Theorem
1.1
in the Planar Case
............................ 68
References
........................................................ 74
xii Contents
Part
ΠΙ
Regularizing Effect of Nonlinearity
in Multidimensional Scalar Conservation Laws
...................... 77
Gianluca Crippa, Felix Otto, and Michael
Westdickenberg
1
Introduction
.................................................... 77
2
Background Material
............................................ 79
3
Entropy Solutions with BV-Regularity
.............................. 84
4
Structure of Entropy Solutions
.................................... 87
5
Kinetic Formulation, Blow-Ups and Split States
...................... 91
6
Classification of Split States
...................................... 98
6.1
Special Split States: No Entropy Dissipation
.................... 98
6.2
Special Split States:
ν
Supported on
a
Hyperplane...............101
6.3
Special Split States:
ν
Supported on Half
a
Hyperplane...........103
6.4
Classification of General Split States
..........................105
7
Proof of the Main Theorem
.......................................106
8
Proofs of the Regularity Theorems
.................................112
References
........................................................128
|
| adam_txt |
Contents
Parti
Existence, Uniqueness, Stability and Differentiability Properties
of the Flow Associated to Weakly Differentiable Vector Fields
. 3
Luigi Ambrosio
and Gianluca Crippa
1
Introduction
. 3
2
The Continuity Equation
. 5
3
The Continuity Equation Within the Cauchy-Lipschitz Framework
. 7
4
(ODE) Uniqueness Vs. (PDE) Uniqueness
. 11
5
The Flow Associated to Sobolev or
B V
Vector Fields
. 19
6
Measure-Theoretic Differentials
. 32
7
Differentiability of the Flow in the W1'1 Case
. 38
8
Differentiability and Compactness of the Flow in the W1'? Case
. 40
9
Bibliographical Notes and Open Problems
. 52
References
. 54
Part
Π
A Note on Alberti's Rank-One Theorem
. 61
Camfflo
De Leilis
1
Introduction
. 61
2
Dimensional Reduction
. 63
3
A Blow-Up Argument Leading to a Partial Result
. 65
4
The Fundamental Lemma
. 66
5
Proof of Theorem
1.1
in the Planar Case
. 68
References
. 74
xii Contents
Part
ΠΙ
Regularizing Effect of Nonlinearity
in Multidimensional Scalar Conservation Laws
. 77
Gianluca Crippa, Felix Otto, and Michael
Westdickenberg
1
Introduction
. 77
2
Background Material
. 79
3
Entropy Solutions with BV-Regularity
. 84
4
Structure of Entropy Solutions
. 87
5
Kinetic Formulation, Blow-Ups and Split States
. 91
6
Classification of Split States
. 98
6.1
Special Split States: No Entropy Dissipation
. 98
6.2
Special Split States:
ν
Supported on
a
Hyperplane.101
6.3
Special Split States:
ν
Supported on Half
a
Hyperplane.103
6.4
Classification of General Split States
.105
7
Proof of the Main Theorem
.106
8
Proofs of the Regularity Theorems
.112
References
.128 |
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| any_adam_object_boolean | 1 |
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| dewey-sort | 3515.3535 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)1071861417 Konferenzschrift 2005 Bologna gnd-content |
| genre_facet | Konferenzschrift 2005 Bologna |
| id | DE-604.BV023357571 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:07:52Z |
| indexdate | 2024-07-09T21:16:45Z |
| institution | BVB |
| isbn | 9783540767800 3540767800 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016541084 |
| oclc_num | 227008458 |
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| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XIV, 130 S. graph. Darst. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer [u.a.] |
| record_format | marc |
| series | Lecture notes of the Unione Matematica Italiana |
| series2 | Lecture notes of the Unione Matematica Italiana |
| spelling | Transport equations and multi-D hyperbolic conservation laws Luigi Ambrosio ... Ed. Fabio Ancona ... Berlin [u.a.] Springer [u.a.] 2008 XIV, 130 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes of the Unione Matematica Italiana 5 Literaturangaben Geometrische Maßtheorie (DE-588)4125258-5 gnd rswk-swf Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2005 Bologna gnd-content Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 s Geometrische Maßtheorie (DE-588)4125258-5 s DE-604 Ambrosio, Luigi 1963- Sonstige (DE-588)133791408 oth Lecture notes of the Unione Matematica Italiana 5 (DE-604)BV022297190 5 http://d-nb.info/987389114/04 Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016541084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Transport equations and multi-D hyperbolic conservation laws Lecture notes of the Unione Matematica Italiana Geometrische Maßtheorie (DE-588)4125258-5 gnd Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd |
| subject_GND | (DE-588)4125258-5 (DE-588)4228136-2 (DE-588)1071861417 |
| title | Transport equations and multi-D hyperbolic conservation laws |
| title_auth | Transport equations and multi-D hyperbolic conservation laws |
| title_exact_search | Transport equations and multi-D hyperbolic conservation laws |
| title_exact_search_txtP | Transport equations and multi-D hyperbolic conservation laws |
| title_full | Transport equations and multi-D hyperbolic conservation laws Luigi Ambrosio ... Ed. Fabio Ancona ... |
| title_fullStr | Transport equations and multi-D hyperbolic conservation laws Luigi Ambrosio ... Ed. Fabio Ancona ... |
| title_full_unstemmed | Transport equations and multi-D hyperbolic conservation laws Luigi Ambrosio ... Ed. Fabio Ancona ... |
| title_short | Transport equations and multi-D hyperbolic conservation laws |
| title_sort | transport equations and multi d hyperbolic conservation laws |
| topic | Geometrische Maßtheorie (DE-588)4125258-5 gnd Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd |
| topic_facet | Geometrische Maßtheorie Nichtlineare hyperbolische Differentialgleichung Konferenzschrift 2005 Bologna |
| url | http://d-nb.info/987389114/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016541084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022297190 |
| work_keys_str_mv | AT ambrosioluigi transportequationsandmultidhyperbolicconservationlaws |
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