Multidimensional hyperbolic partial differential equations: first-order systems and applications
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Clarendon Press
2007
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| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Beschreibung für Leser Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXV, 508 S. graph. Darst. |
| ISBN: | 019921123X 9780199211234 |
Internformat
MARC
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| 049 | |a DE-703 |a DE-824 |a DE-355 |a DE-634 |a DE-11 |a DE-384 | ||
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| 084 | |a SK 560 |0 (DE-625)143246: |2 rvk | ||
| 100 | 1 | |a Benzoni-Gavage, Sylvie |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multidimensional hyperbolic partial differential equations |b first-order systems and applications |c Sylvie Benzoni-Gavage ; Denis Serre |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Clarendon Press |c 2007 | |
| 300 | |a XXV, 508 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford mathematical monographs | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Équations différentielles hyperboliques | |
| 650 | 4 | |a Differential equations, Hyperbolic | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 0 | 7 | |a Hyperbolische Differentialgleichung |0 (DE-588)4131213-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a System von partiellen Differentialgleichungen |0 (DE-588)4116672-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ordnung 1 |0 (DE-588)4372621-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hyperbolische Differentialgleichung |0 (DE-588)4131213-2 |D s |
| 689 | 0 | 1 | |a System von partiellen Differentialgleichungen |0 (DE-588)4116672-3 |D s |
| 689 | 0 | 2 | |a Ordnung 1 |0 (DE-588)4372621-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Serre, Denis |d 1954- |e Sonstige |0 (DE-588)173306659 |4 oth | |
| 856 | 4 | |u http://www.gbv.de/dms/goettingen/516826956.pdf |3 Inhaltsverzeichnis | |
| 856 | 4 | |u http://catdir.loc.gov/catdir/enhancements/fy0726/2007295111-d.html |3 Beschreibung für Leser | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015052105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804135774348640256 |
|---|---|
| adam_text | CONTENTS
Preface
Introduction
xiii
Notations
XXI
PART I. THE LINEAR CAUCHY PROBLEM
1
Linear Cauchy Problem with Constant Coefficients
3
1.1
Very weak well-posedness
4
1.2
Strong well-posedness
7
1.2.1
Hyperbolicity
7
1.2.2
Distributional solutions
9
1.2.3
The Kreiss matrix Theorem
10
1.2.4
Two important classes of hyperbolic systems
13
1.2.5
The adjoint operator
15
1.2.6
Classical solutions
15
1.2.7
Well-posedness in Lebesgue spaces
16
1.3
Friedrichs-symmetrizable systems
17
1.3.1
Dependence and influence cone
18
1.3.2
Non-decaying data
20
1.3.3
Uniqueness for non-decaying data
21
1.4
Directions of hyperbolicity
23
1.4.1
Properties of the eigenvalues
23
1.4.2
The characteristic and forward cones
26
1.4.3
Change of variables
27
1.4.4
Homogeneous hyperbolic polynomials
30
1.5
Miscellaneous
32
1.5.1
Hyperbolicity of subsystems
32
1.5.2
Strichartz estimates
36
1.5.3
Systems with differential constraints
41
1.5.4
Splitting of the characteristic polynomial
45
1.5.5
Dimensional restrictions for strictly hyperbolic systems
47
1.5.6
Realization of hyperbolic polynomial
48
viii Contents
2
Linear Cauchy problem
with variable coefficients
50
2.1
Well-posedness
in Sobolev spaces
51
2.1.1
Energy
estimates in the scalar case
51
2.1.2
Symmetrizers and energy estimates
52
2.1.3
Energy estimates for less-smooth coefficients
58
2.1.4
How energy estimates imply well-posedness
63
2.2
Local uniqueness and finite-speed propagation
72
2.3
Non-decaying infinitely smooth data
80
2.4
Weighted in time estimates
81
PART II. THE LINEAR INITIAL BOUNDARY
VALUE PROBLEM
3
Friedrichs-symmetric dissipative IBVPs
85
3.1
The weakly dissipative case
85
3.1.1
Traces
88
3.1.2
Monotonicity
of A
89
3.1.3
Maximality of A
90
3.2
Strictly dissipative symmetric IBVPs
93
3.2.1
The a priori estimate
95
3.2.2
Construction of
û
and
и
96
Initial boundary value problem in a half-space with constant
coefficients
99
4.1
Position of the problem
99
4.1.1
The number of scalar boundary conditions
100
4.1.2
Normal IBVP
102
4.2
The
Kreiss-Lopatinskiï
condition
102
4.2.1
The non-characteristic case
103
4.2.2
Well-posedness in Sobolev spaces
106
4.2.3
The characteristic case
107
4.3
The uniform
Kreiss-Lopatinskiï
condition
109
4.3.1
A necessary condition for strong well-posedness
109
4.3.2
The characteristic IBVP 111
4.3.3
An equivalent formulation of (UKL)
112
4.3.4
Example: The dissipative symmetric case
113
4.4
The adjoint IBVP
114
4.5
Main results in the non-characteristic case
118
4.5.1
Kreiss symmetrizers
119
4.5.2
Fundamental estimates
120
4.5.3
Existence and uniqueness for the boundary value
problem in
.Ц
123
4.5.4
Improved estimates
125
Contents
¡χ
4.5.5
Existence
for the initial boundary value problem
126
4.5.6
Proof of Theorem
4.3 128
4.5.7
Summary
129
4.5.8
Comments
129
4.6
A practical tool
130
4.6.1
The
Lopatinskiï
determinant
130
4.6.2
Algebraicity of the
Lopatinskiï
determinant
133
4.6.3
A geometrical view of (UKL) condition
136
4.6.4
The
Lopatinskiï
determinant of the adjoint IBVP
137
5
Construction of a symmetrizer under (UKL)
139
5.1
The block structure at boundary points
139
5.1.1
Proof of Lemma
4.5 139
5.1.2
The block structure
141
5.2
Construction of a Kreiss symmetrizer under (UKL)
144
6
The characteristic IBVP
158
6.1
Facts about the characteristic case
158
6.1.1
A necessary condition for strong well-posedness
159
6.1.2
The case of a linear eigenvalue
162
6.1.3
Facts in two space dimensions
167
6.1.4
The space
Ε- (Ο,τ?)
169
6.1.5
Conclusion
174
6.1.6
Ohkubo s case
175
6.2
Construction of the symmetrizer; characteristic case
176
7
The homogeneous IBVP
182
7.1
Necessary conditions for strong well-posedness
184
7.1.1
An illustration: the wave equation
189
7.2
Weakly dissipative symmetrizer
191
7.3
Surface waves of finite energy
196
8
A classification of linear IBVPs
201
8.1
Some obvious robust classes
202
8.2
Frequency boundary points
202
8.2.1
Hyperbolic boundary points
203
8.2.2
On the continuation of
Ε-{τ, η)
205
8.2.3
Glancing points
207
8.2.4
The
Lopatinskiï
determinant along the boundary
208
8.3
Weakly well-posed IBVPs of real type
208
8.3.1
The adjoint problem of a BVP of class WR
210
8.4
Well-posedness of unsual type for BVPs of class WR
211
Contents
8.4.1
A
priori
estimates (I)
211
8.4.2
A priori estimates (II)
214
8.4.3
The estimate for the adjoint BVP
216
8.4.4
Existence result for the BVP
217
8.4.5
Propagation property
218
9
Variable-coeflicients initial boundary value problems
220
9.1
Energy estimates
222
9.1.1
Functional boundary symmetrizers
225
9.1.2
Local/global Kreiss symmetrizers
229
9.1.3
Construction of local Kreiss symmetrizers
233
9.1.4
Non-planar boundaries
242
9.1.5
Less-smooth coefficients
245
9.2
How energy estimates imply well-posedness
255
9.2.1
The Boundary Value Problem
255
9.2.2
The homogeneous IBVP
264
9.2.3
The general IBVP (smooth coefficients)
267
9.2.4
Rough coefficients
271
9.2.5
Coefficients of limited regularity
281
PART III. NON-LINEAR PROBLEMS
10
The Cauchy problem for
quasilinear
systems
291
10.1
Smooth solutions
292
10.1.1
Local well-posedness
292
10.1.2
Continuation of solutions
302
10.2
Weak solutions
304
10.2.1
Entropy solutions
305
10.2.2
Piecewise smooth solutions
311
11
The mixed problem for
quasilinear
systems
315
11.1
Main results
316
11.1.1
Structural and stability assumptions
316
11.1.2
Conditions on the data
318
11.1.3
Local solutions of the mixed problem
319
11.1.4
Well-posedness of the mixed problem
320
11.2
Proofs
321
11.2.1
Technical material
321
11.2.2
Proof of Theorem
11.1 326
12
Persistence of multidimensional shocks
329
12.1
From FBP to IBVP
331
Contents
12.1.1
The non-linear problem
331
12.1.2
Fixing the boundary
332
12.1.3
Linearized problems
334
12.2
Normal modes analysis
337
12.2.1
Comparison with standard IBVP
337
12.2.2
Nature of shocks
341
12.2.3
The generalized Kreiss-Lopatinskii condition
344
12.3
Well-posedness of linearized problems
345
12.3.1
Energy estimates for the BVP
345
12.3.2
Adjoint BVP
355
12.3.3
Well-posedness of the BVP
360
12.3.4
The IBVP with zero initial data
366
12.4
Resolution of non-linear IBVP
368
12.4.1
Planar reference shocks
368
12.4.2
Compact shock fronts
374
PART IV. APPLICATIONS TO GAS DYNAMICS
13
The
Euler
equations for real fluids
385
13.1
Thermodynamics
385
13.2
The
Euler
equations
391
13.2.1
Derivation and comments
391
13.2.2
Hyperbolicity
392
13.2.3
Symmetrizability
394
13.3
The Cauchy problem
399
13.4
Shock waves
399
13.4.1
The Rankine-Hugoniot condition
399
13.4.2
The Hugoniot adiabats
401
13.4.3
Admissibility criteria
401
14
Boundary conditions for
Euler
equations
411
14.1
Classification of fluids IBVPs
411
14.2
Dissipative initial boundary value problems
412
14.3
Normal modes analysis
414
14.3.1
The stable subspace of interior equations
414
14.3.2
Derivation of the
Lopatinskiï
determinant
416
14.4
Construction of a Kreiss symmetrizer
419
15
Shock stability in gas dynamics
424
15.1
Normal modes analysis
424
15.1.1
The stable subspace for interior equations
425
15.1.2
The linearized jump conditions
426
15.1.3
The
Lopatinskiï
determinant
427
xii Contents
15.2
Stability conditions
430
15.2.1
General result
430
15.2.2
Notable cases
437
15.2.3
Kreiss symmetrizers
438
15.2.4
Weak stability
440
PART V. APPENDIX
A Basic calculus results
443
В
Fourier and Laplace analysis
446
B.I Fourier transform
446
B.2 Laplace transform
447
B.3 Fourier-Laplace transform
448
С
Pseudi^/para-differential calculus
449
C.I Pseudo-differential calculus
450
C.I.I Symbols and approximate symbols
450
C.I.
2
Definition of pseudo-differential operators
452
C.1.3 Basic properties of pseudo-differential operators
453
C.2 Pseudo-differential calculus with a parameter
455
C.3 Littlewood-Paley decomposition
459
C.3.1 Introduction
459
C.3.
2
Basic estimates concerning Sobolev spaces
461
C.3.3 Para-products
465
C.3.
4
Para-linearization
473
C.3.5 Further estimates
478
C.4 Para-differential calculus
481
C.4.1 Construction of para-differential operators
481
C.4.
2
Basic results
486
C.5 Parar-differential calculus with a parameter
487
Bibliography
492
Index
505
|
| adam_txt |
CONTENTS
Preface
Introduction
xiii
Notations
XXI
PART I. THE LINEAR CAUCHY PROBLEM
1
Linear Cauchy Problem with Constant Coefficients
3
1.1
Very weak well-posedness
4
1.2
Strong well-posedness
7
1.2.1
Hyperbolicity
7
1.2.2
Distributional solutions
9
1.2.3
The Kreiss' matrix Theorem
10
1.2.4
Two important classes of hyperbolic systems
13
1.2.5
The adjoint operator
15
1.2.6
Classical solutions
15
1.2.7
Well-posedness in Lebesgue spaces
16
1.3
Friedrichs-symmetrizable systems
17
1.3.1
Dependence and influence cone
18
1.3.2
Non-decaying data
20
1.3.3
Uniqueness for non-decaying data
21
1.4
Directions of hyperbolicity
23
1.4.1
Properties of the eigenvalues
23
1.4.2
The characteristic and forward cones
26
1.4.3
Change of variables
27
1.4.4
Homogeneous hyperbolic polynomials
30
1.5
Miscellaneous
32
1.5.1
Hyperbolicity of subsystems
32
1.5.2
Strichartz estimates
36
1.5.3
Systems with differential constraints
41
1.5.4
Splitting of the characteristic polynomial
45
1.5.5
Dimensional restrictions for strictly hyperbolic systems
47
1.5.6
Realization of hyperbolic polynomial
48
viii Contents
2
Linear Cauchy problem
with variable coefficients
50
2.1
Well-posedness
in Sobolev spaces
51
2.1.1
Energy
estimates in the scalar case
51
2.1.2
Symmetrizers and energy estimates
52
2.1.3
Energy estimates for less-smooth coefficients
58
2.1.4
How energy estimates imply well-posedness
63
2.2
Local uniqueness and finite-speed propagation
72
2.3
Non-decaying infinitely smooth data
80
2.4
Weighted in time estimates
81
PART II. THE LINEAR INITIAL BOUNDARY
VALUE PROBLEM
3
Friedrichs-symmetric dissipative IBVPs
85
3.1
The weakly dissipative case
85
3.1.1
Traces
88
3.1.2
Monotonicity
of A
89
3.1.3
Maximality of A
90
3.2
Strictly dissipative symmetric IBVPs
93
3.2.1
The a priori estimate
95
3.2.2
Construction of
û
and
и
96
Initial boundary value problem in a half-space with constant
coefficients
99
4.1
Position of the problem
99
4.1.1
The number of scalar boundary conditions
100
4.1.2
Normal IBVP
102
4.2
The
Kreiss-Lopatinskiï
condition
102
4.2.1
The non-characteristic case
103
4.2.2
Well-posedness in Sobolev spaces
106
4.2.3
The characteristic case
107
4.3
The uniform
Kreiss-Lopatinskiï
condition
109
4.3.1
A necessary condition for strong well-posedness
109
4.3.2
The characteristic IBVP 111
4.3.3
An equivalent formulation of (UKL)
112
4.3.4
Example: The dissipative symmetric case
113
4.4
The adjoint IBVP
114
4.5
Main results in the non-characteristic case
118
4.5.1
Kreiss' symmetrizers
119
4.5.2
Fundamental estimates
120
4.5.3
Existence and uniqueness for the boundary value
problem in
.Ц
123
4.5.4
Improved estimates
125
Contents
¡χ
4.5.5
Existence
for the initial boundary value problem
126
4.5.6
Proof of Theorem
4.3 128
4.5.7
Summary
129
4.5.8
Comments
129
4.6
A practical tool
130
4.6.1
The
Lopatinskiï
determinant
130
4.6.2
'Algebraicity' of the
Lopatinskiï
determinant
133
4.6.3
A geometrical view of (UKL) condition
136
4.6.4
The
Lopatinskiï
determinant of the adjoint IBVP
137
5
Construction of a symmetrizer under (UKL)
139
5.1
The block structure at boundary points
139
5.1.1
Proof of Lemma
4.5 139
5.1.2
The block structure
141
5.2
Construction of a Kreiss symmetrizer under (UKL)
144
6
The characteristic IBVP
158
6.1
Facts about the characteristic case
158
6.1.1
A necessary condition for strong well-posedness
159
6.1.2
The case of a linear eigenvalue
162
6.1.3
Facts in two space dimensions
167
6.1.4
The space
Ε- (Ο,τ?)
169
6.1.5
Conclusion
174
6.1.6
Ohkubo's case
175
6.2
Construction of the symmetrizer; characteristic case
176
7
The homogeneous IBVP
182
7.1
Necessary conditions for strong well-posedness
184
7.1.1
An illustration: the wave equation
189
7.2
Weakly dissipative symmetrizer
191
7.3
Surface waves of finite energy
196
8
A classification of linear IBVPs
201
8.1
Some obvious robust classes
202
8.2
Frequency boundary points
202
8.2.1
Hyperbolic boundary points
203
8.2.2
On the continuation of
Ε-{τ, η)
205
8.2.3
Glancing points
207
8.2.4
The
Lopatinskiï
determinant along the boundary
208
8.3
Weakly well-posed IBVPs of real type
208
8.3.1
The adjoint problem of a BVP of class WR
210
8.4
Well-posedness of unsual type for BVPs of class WR
211
Contents
8.4.1
A
priori
estimates (I)
211
8.4.2
A priori estimates (II)
214
8.4.3
The estimate for the adjoint BVP
216
8.4.4
Existence result for the BVP
217
8.4.5
Propagation property
218
9
Variable-coeflicients initial boundary value problems
220
9.1
Energy estimates
222
9.1.1
Functional boundary symmetrizers
225
9.1.2
Local/global Kreiss' symmetrizers
229
9.1.3
Construction of local Kreiss' symmetrizers
233
9.1.4
Non-planar boundaries
242
9.1.5
Less-smooth coefficients
245
9.2
How energy estimates imply well-posedness
255
9.2.1
The Boundary Value Problem
255
9.2.2
The homogeneous IBVP
264
9.2.3
The general IBVP (smooth coefficients)
267
9.2.4
Rough coefficients
271
9.2.5
Coefficients of limited regularity
281
PART III. NON-LINEAR PROBLEMS
10
The Cauchy problem for
quasilinear
systems
291
10.1
Smooth solutions
292
10.1.1
Local well-posedness
292
10.1.2
Continuation of solutions
302
10.2
Weak solutions
304
10.2.1
Entropy solutions
305
10.2.2
Piecewise smooth solutions
311
11
The mixed problem for
quasilinear
systems
315
11.1
Main results
316
11.1.1
Structural and stability assumptions
316
11.1.2
Conditions on the data
318
11.1.3
Local solutions of the mixed problem
319
11.1.4
Well-posedness of the mixed problem
320
11.2
Proofs
321
11.2.1
Technical material
321
11.2.2
Proof of Theorem
11.1 326
12
Persistence of multidimensional shocks
329
12.1
From FBP to IBVP
331
Contents
12.1.1
The non-linear problem
331
12.1.2
Fixing the boundary
332
12.1.3
Linearized problems
334
12.2
Normal modes analysis
337
12.2.1
Comparison with standard IBVP
337
12.2.2
Nature of shocks
341
12.2.3
The generalized Kreiss-Lopatinskii condition
344
12.3
Well-posedness of linearized problems
345
12.3.1
Energy estimates for the BVP
345
12.3.2
Adjoint BVP
355
12.3.3
Well-posedness of the BVP
360
12.3.4
The IBVP with zero initial data
366
12.4
Resolution of non-linear IBVP
368
12.4.1
Planar reference shocks
368
12.4.2
Compact shock fronts
374
PART IV. APPLICATIONS TO GAS DYNAMICS
13
The
Euler
equations for real fluids
385
13.1
Thermodynamics
385
13.2
The
Euler
equations
391
13.2.1
Derivation and comments
391
13.2.2
Hyperbolicity
392
13.2.3
Symmetrizability
394
13.3
The Cauchy problem
399
13.4
Shock waves
399
13.4.1
The Rankine-Hugoniot condition
399
13.4.2
The Hugoniot adiabats
401
13.4.3
Admissibility criteria
401
14
Boundary conditions for
Euler
equations
411
14.1
Classification of fluids IBVPs
411
14.2
Dissipative initial boundary value problems
412
14.3
Normal modes analysis
414
14.3.1
The stable subspace of interior equations
414
14.3.2
Derivation of the
Lopatinskiï
determinant
416
14.4
Construction of a Kreiss symmetrizer
419
15
Shock stability in gas dynamics
424
15.1
Normal modes analysis
424
15.1.1
The stable subspace for interior equations
425
15.1.2
The linearized jump conditions
426
15.1.3
The
Lopatinskiï
determinant
427
xii Contents
15.2
Stability conditions
430
15.2.1
General result
430
15.2.2
Notable cases
437
15.2.3
Kreiss symmetrizers
438
15.2.4
Weak stability
440
PART V. APPENDIX
A Basic calculus results
443
В
Fourier and Laplace analysis
446
B.I Fourier transform
446
B.2 Laplace transform
447
B.3 Fourier-Laplace transform
448
С
Pseudi^/para-differential calculus
449
C.I Pseudo-differential calculus
450
C.I.I Symbols and approximate symbols
450
C.I.
2
Definition of pseudo-differential operators
452
C.1.3 Basic properties of pseudo-differential operators
453
C.2 Pseudo-differential calculus with a parameter
455
C.3 Littlewood-Paley decomposition
459
C.3.1 Introduction
459
C.3.
2
Basic estimates concerning Sobolev spaces
461
C.3.3 Para-products
465
C.3.
4
Para-linearization
473
C.3.5 Further estimates
478
C.4 Para-differential calculus
481
C.4.1 Construction of para-differential operators
481
C.4.
2
Basic results
486
C.5 Parar-differential calculus with a parameter
487
Bibliography
492
Index
505 |
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| any_adam_object_boolean | 1 |
| author | Benzoni-Gavage, Sylvie |
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| callnumber-label | QA374 |
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| callnumber-search | QA374 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 500 SK 560 |
| ctrlnum | (OCoLC)71163824 (DE-599)BVBBV021840238 |
| dewey-full | 515.353 |
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| 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 |
| edition | 1. publ. |
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| id | DE-604.BV021840238 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:00:12Z |
| indexdate | 2024-07-09T20:45:51Z |
| institution | BVB |
| isbn | 019921123X 9780199211234 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015052105 |
| oclc_num | 71163824 |
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| physical | XXV, 508 S. graph. Darst. |
| publishDate | 2007 |
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| publishDateSort | 2007 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Benzoni-Gavage, Sylvie Verfasser aut Multidimensional hyperbolic partial differential equations first-order systems and applications Sylvie Benzoni-Gavage ; Denis Serre 1. publ. Oxford [u.a.] Clarendon Press 2007 XXV, 508 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Includes bibliographical references and index Équations aux dérivées partielles Équations différentielles hyperboliques Differential equations, Hyperbolic Differential equations, Partial Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd rswk-swf Ordnung 1 (DE-588)4372621-5 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 s System von partiellen Differentialgleichungen (DE-588)4116672-3 s Ordnung 1 (DE-588)4372621-5 s DE-604 Serre, Denis 1954- Sonstige (DE-588)173306659 oth http://www.gbv.de/dms/goettingen/516826956.pdf Inhaltsverzeichnis http://catdir.loc.gov/catdir/enhancements/fy0726/2007295111-d.html Beschreibung für Leser Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015052105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benzoni-Gavage, Sylvie Multidimensional hyperbolic partial differential equations first-order systems and applications Équations aux dérivées partielles Équations différentielles hyperboliques Differential equations, Hyperbolic Differential equations, Partial Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd Ordnung 1 (DE-588)4372621-5 gnd |
| subject_GND | (DE-588)4131213-2 (DE-588)4116672-3 (DE-588)4372621-5 |
| title | Multidimensional hyperbolic partial differential equations first-order systems and applications |
| title_auth | Multidimensional hyperbolic partial differential equations first-order systems and applications |
| title_exact_search | Multidimensional hyperbolic partial differential equations first-order systems and applications |
| title_exact_search_txtP | Multidimensional hyperbolic partial differential equations first-order systems and applications |
| title_full | Multidimensional hyperbolic partial differential equations first-order systems and applications Sylvie Benzoni-Gavage ; Denis Serre |
| title_fullStr | Multidimensional hyperbolic partial differential equations first-order systems and applications Sylvie Benzoni-Gavage ; Denis Serre |
| title_full_unstemmed | Multidimensional hyperbolic partial differential equations first-order systems and applications Sylvie Benzoni-Gavage ; Denis Serre |
| title_short | Multidimensional hyperbolic partial differential equations |
| title_sort | multidimensional hyperbolic partial differential equations first order systems and applications |
| title_sub | first-order systems and applications |
| topic | Équations aux dérivées partielles Équations différentielles hyperboliques Differential equations, Hyperbolic Differential equations, Partial Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd Ordnung 1 (DE-588)4372621-5 gnd |
| topic_facet | Équations aux dérivées partielles Équations différentielles hyperboliques Differential equations, Hyperbolic Differential equations, Partial Hyperbolische Differentialgleichung System von partiellen Differentialgleichungen Ordnung 1 |
| url | http://www.gbv.de/dms/goettingen/516826956.pdf http://catdir.loc.gov/catdir/enhancements/fy0726/2007295111-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015052105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT benzonigavagesylvie multidimensionalhyperbolicpartialdifferentialequationsfirstordersystemsandapplications AT serredenis multidimensionalhyperbolicpartialdifferentialequationsfirstordersystemsandapplications |
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