Global propagation of regular nonlinear hyperbolic waves:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2009
|
| Series: | Progress in Nonlinear Differential Equations and their Applications
76 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 252 S. 235 mm x 155 mm, 549 gr. |
| ISBN: | 9780817642440 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS PREFACE V I INTRODUCTION 1 1.1 CAUCHY PROBLEM 1 1.2 WEAK LINEAR
DEGENERACY 5 1.3 SOME EXAMPLES 7 1.3.1 SYSTEM OF NONLINEAR ELASTICITY 7
1.3.2 SYSTEM OF TRAFFIC FLOW 8 1.3.3 SYSTEM OF ONE-DIMENSIONAL GAS
DYNAMICS 9 1.3.4 SYSTEM OF COMPRESSIBLE ELASTIC FLUIDS WITH MEMORY 11
1.3.5 SYSTEM OF THE MOTION OF AN ELASTIC STRING 13 1.3.6 SYSTEM OF
FINITE AMPLITUDE PLANE ELASTIC WAVES FOR HYPERELASTIC MATERIALS 15 1.4
MAIN RESULTS FOR THE CAUCHY PROBLEM 16 1.5 NORMALIZED COORDINATES 18 1.6
WEAK LINEAR DEGENERACY AND GENERALIZED NULL CONDITION.. 19 1.7
NONSTRICTLY HYPERBOLIC CASE 20 1.8 CAUCHY PROBLEM ON A SEMIBOUNDED
INITIAL AXIS 21 1.9 ONE-SIDED MIXED INITIAL-BOUNDARY VALUE PROBLEM 22
1.10 GENERALIZED RIEMANN PROBLEM 23 1.11 GENERALIZED NONLINEAR
INITIAL-BOUNDARY RIEMANN PROBLEM . 24 1.12 INVERSE GENERALIZED RIEMANN
PROBLEM 26 1.13 INVERSE PISTON PROBLEM 26 II PRELIMINARIES 29 2.1
DEFINITION OF QUASILINEAR HYPERBOLIC SYSTEM 29 2.2 INVARIANCE UNDER A
SMOOTH INVERTIBLE TRANSFORMATION OF UNKNOWN VARIABLES 31 2.3 GENUINE
NONLINEARITY AND LINEAR DEGENERACY 33 2.4 NORMALIZED COORDINATES 34
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/995050961 DIGITALISIERT
DURCH VIII CONTENTS 2.4.1 NORMALIZED COORDINATES FOR STRICTLY HYPERBOLIC
SYSTEMS 34 2.4.2 NORMALIZED COORDINATES FOR NONSTRICTLY HYPERBOLIC
SYSTEMS WITH CHARACTERISTICS WITH CONSTANT MULTIPLICITY 36 2.4.3
GENERALIZED NORMALIZED COORDINATES FOR GENERAL HYPERBOLIC SYSTEMS 37 2.5
WEAK LINEAR DEGENERACY 38 2.5.1 WEAK LINEAR DEGENERACY FOR STRICTLY
HYPERBOLIC SYSTEMS 38 2.5.2 WEAK LINEAR DEGENERACY FOR NONSTRICTLY
HYPERBOLIC SYSTEMS WITH CHARACTERISTICS WITH CONSTANT MULTIPLICITY 40
2.5.3 WEAK LINEAR DEGENERACY FOR GENERAL HYPERBOLIC SYSTEMS 40 2.6
DECOMPOSITION OF WAVES 41 2.6.1 FORMULAS ON THE DECOMPOSITION OF WAVES
41 2.6.2 FORMULAS ON THE DECOMPOSITION OF WAVES (CONTINUED) 45 2.7 TWO
LEMMAS ON ORDINARY DIFFERENTIAL EQUATIONS 48 III THE CAUCHY PROBLEM 51
3.1 NECESSARY CONDITION TO GUARANTEE THE GLOBAL EXISTENCE AND UNIQUENESS
OF THE C 1 SOLUTION TO THE CAUCHY PROBLEM FOR THE STRICTLY HYPERBOLIC
SYSTEM 51 3.2 SOME UNIFORM A PRIORI ESTIMATES INDEPENDENT OF NORMALIZED
COORDINATES AND WEAK LINEAR DEGENERACY FOR THE STRICTLY HYPERBOLIC
SYSTEM 54 3.3 SOME UNIFORM A PRIORI ESTIMATES DEPENDING ON NORMALIZED
COORDINATES AND WEAK LINEAR DEGENERACY FOR THE STRICTLY HYPERBOLIC
SYSTEM 60 3.4 SUFFICIENT CONDITION TO GUARANTEE THE GLOBAL EXISTENCE AND
UNIQUENESS OF THE C 1 CONTENTS X IV THE CAUCHY PROBLEM (CONTINUED) 79
4.1 SOME UNIFORM A PRIORI ESTIMATES INDEPENDENT OF WEAK LINEAR
DEGENERACY 7!) 4.2 FORMATION OF SINGULARITIES OF THE C 1 SOLUTION IN THE
NONCRITICAL CASE A +OC 80 4.2.1 SOME UNIFORM A PRIORI ESTIMATES
DEPENDING ON WEAK LINEAR DEGENERACY 80 4.2.2 SHARP ESTIMATE ON THE LIFE
SPAN OF THE C 1 SOLUTION 84 4.3 BLOW-UP MECHANISM OF THE C L SOLUTION IN
THE NONCRITICAL CASE O +OO 92 4.3.1 INTRODUCTION AND MAIN RESULTS 92
4.3.2 PROOF OF MAIN RESULTS 93 4.4 APPLICATIONS 100 4.4.1 SYSTEM OF
TRAFFIC FLOW 100 4.4.2 SYSTEM OF ONE-DIMENSIONAL GAS DYNAMICS 102 4.4.3
SYSTEM OF COMPRESSIBLE ELASTIC FLUIDS WITH MEMORY 104 4.5 BLOW-UP
MECHANISM OF THE C 1 SOLUTION IN THE CRITICAL CASE A = +OC 106 4.5.1
INTRODUCTION AND MAIN RESULTS 106 4.5.2 SOME UNIFORM A PRIORI ESTIMATES
DEPENDING ON WEAK LINEAR DEGENERACY 107 4.5.3 PROOF OF MAIN RESULTS 110
4.6 REMARKS 113 V CAUCHY PROBLEM ON A SEMIBOUNDED INITIAL AXIS 115 5.1
INTRODUCTION AND MAIN RESULTS 115 5.2 PROOF OF THEOREM 5.1.1 117 5.3
APPLICATION 124 VI ONE-SIDED MIXED INITIAL-BOUNDARY VALUE PROBLEM 12 X
CONTENTS 7.2.1 DECOMPOSITION OF WAVES 154 7.2.2 RANKINE-HUGONIOT
CONDITION 155 7.3 PROOF OF MAIN RESULTS 158 7.4 APPLICATIONS 169 7.4.1
SYSTEM OF TRAFFIC FLOW 169 7.4.2 SYSTEM OF ONE-DIMENSIONAL GAS DYNAMICS
171 7.4.3 SYSTEM OF PLANE ELASTIC WAVES FOR HYPERELASTIC MATERIAL 172
VIII GENERALIZED NONLINEAR INITIAL-BOUNDARY RIEMANN PROBLEM 175 8.1
INTRODUCTION AND MAIN RESULTS 175 8.2 PRELIMINARIES 179 8.3 PROOF OF
THEOREM 8.1.1 180 8.4 PROOF OF THEOREM 8.1.2 182 IX INVERSE GENERALIZED
RIEMANN PROBLEM 191 9.1 INTRODUCTION AND MAIN RESULTS 191 9.2
GENERALIZED CAUCHY PROBLEM 195 9.3 PROOF OF THEOREM 9.1.1 202 X INVERSE
PISTON PROBLEM 209 10.1 INVERSE PISTON PROBLEM FOR THE SYSTEM OF
ONE-DIMENSIONAL ISENTROPIC FLOW 209 10.1.1 INTRODUCTION AND MAIN RESULTS
209 10.1.2 PROOF OF THEOREM 10.1.1 215 10.1.3 RELATED PROBLEM IN
EULERIAN REPRESENTATION 223 10.2 GENERALIZED CAUCHY PROBLEM WITH CAUCHY
DATA GIVEN ON A SEMIBOUNDED NONCHARACTERISTIC CURVE 230 10.3 INVERSE
PISTON PROBLEM FOR THE SYSTEM OF ONE-DIMENSIONAL ADIABATIC FLOW 235
10.3.1 INTRODUCTION 235 10.3.2 INVERSE PISTON PROBLEM IN LAGRANGIAN
REPRESENTATION238 10.3.3 INVERSE PISTON PROBLEM IN EULERIAN
REPRESENTATION . 240 REFERENCES 245 INDE
|
| any_adam_object | 1 |
| author | Li, Daqian 1937- Wang, Libin |
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| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)318675107 (DE-599)DNB995050961 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035674446 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:43:02Z |
| institution | BVB |
| isbn | 9780817642440 |
| language | English |
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| oclc_num | 318675107 |
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| owner_facet | DE-355 DE-BY-UBR |
| physical | X, 252 S. 235 mm x 155 mm, 549 gr. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in Nonlinear Differential Equations and their Applications |
| series2 | Progress in Nonlinear Differential Equations and their Applications |
| spelling | Li, Daqian 1937- Verfasser (DE-588)124460550 aut Global propagation of regular nonlinear hyperbolic waves Li Tatsien ; Wang Libin Boston [u.a.] Birkhäuser 2009 X, 252 S. 235 mm x 155 mm, 549 gr. txt rdacontent n rdamedia nc rdacarrier Progress in Nonlinear Differential Equations and their Applications 76 Hyperbolisches Differentialgleichungssystem - Nichtlineare Welle - Wellenausbreitung Differential equations, Hyperbolic Nonlinear wave equations Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd rswk-swf Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 s Nichtlineare Welle (DE-588)4042102-8 s Wellenausbreitung (DE-588)4121912-0 s DE-604 Wang, Libin Verfasser (DE-588)138832714 aut Progress in Nonlinear Differential Equations and their Applications 76 (DE-604)BV007934389 76 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728672&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Li, Daqian 1937- Wang, Libin Global propagation of regular nonlinear hyperbolic waves Progress in Nonlinear Differential Equations and their Applications Hyperbolisches Differentialgleichungssystem - Nichtlineare Welle - Wellenausbreitung Differential equations, Hyperbolic Nonlinear wave equations Nichtlineare Welle (DE-588)4042102-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd |
| subject_GND | (DE-588)4042102-8 (DE-588)4121912-0 (DE-588)4496581-3 |
| title | Global propagation of regular nonlinear hyperbolic waves |
| title_auth | Global propagation of regular nonlinear hyperbolic waves |
| title_exact_search | Global propagation of regular nonlinear hyperbolic waves |
| title_full | Global propagation of regular nonlinear hyperbolic waves Li Tatsien ; Wang Libin |
| title_fullStr | Global propagation of regular nonlinear hyperbolic waves Li Tatsien ; Wang Libin |
| title_full_unstemmed | Global propagation of regular nonlinear hyperbolic waves Li Tatsien ; Wang Libin |
| title_short | Global propagation of regular nonlinear hyperbolic waves |
| title_sort | global propagation of regular nonlinear hyperbolic waves |
| topic | Hyperbolisches Differentialgleichungssystem - Nichtlineare Welle - Wellenausbreitung Differential equations, Hyperbolic Nonlinear wave equations Nichtlineare Welle (DE-588)4042102-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd |
| topic_facet | Hyperbolisches Differentialgleichungssystem - Nichtlineare Welle - Wellenausbreitung Differential equations, Hyperbolic Nonlinear wave equations Nichtlineare Welle Wellenausbreitung Hyperbolisches Differentialgleichungssystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728672&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
| work_keys_str_mv | AT lidaqian globalpropagationofregularnonlinearhyperbolicwaves AT wanglibin globalpropagationofregularnonlinearhyperbolicwaves |