Explosive instabilities in mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 196 S. graph. Darst. |
| ISBN: | 3540635890 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | BRIAN STRAUGHAN EXPLOSIVE INSTABILITIES IN MECHANICS WITH 12 FIGURES **
SPRINGER CONTENTS 1. INTRODUCTION 1 1.1 BLOW-UP IN PARTIAL DIFFERENTIAL
EQUATIONS IN APPLIED MATHEMATICS 1 1.2 METHODS OF ESTABLISHING
NON-EXISTENCE AND GROWTH SOLUTIONS 4 1.2.1 THE CONCAVITY METHOD 4 1.2.2
THE EIGENFUNCTION METHOD 10 1.2.3 EXPLICIT INEQUALITY METHODS 12 1.2.4
THE MULTI-EIGENFUNCTION METHOD 15 1.2.5 LOGARITHMIC CONVEXITY 17 1.3
FINITE TIME BLOW-UP SYSTEMS WITH CONVECTION 19 1.3.1 FUJITA-TYPE
PROBLEMS 20 1.3.2 EQUATIONS WITH GRADIENT TERMS 24 1.3.3 SYSTEMS WITH
GRADIENT TERMS 27 1.3.4 EQUATIONS WITH GRADIENT TERMS AND NON-DIRICHLET
BOUNDARY CONDITIONS 28 1.3.5 BLOW-UP OF DERIVATIVES 31 2. ANALYSIS OF A
FIRST-ORDER SYSTEM 33 2.1 CONDITIONAL DECAY OF SOLUTIONS 33 2.2
BOUNDEDNESS OF SOLUTIONS 37 2.3 UNCONDITIONAL DECAY OF SOLUTIONS 40
2.3.1 SPECIAL CASES 43 2.4 GLOBAL NON-EXISTENCE OF SOLUTIONS 44 2.5
NUMERICAL RESULTS BY FINITE ELEMENTS 47 2.5.1 SOLUTION STRUCTURE WITH
LINEAR AND QUADRATIC RIGHT-HAND SIDES 47 3. SINGULARITIES FOR CLASSICAL
FLUID EQUATIONS 6 3 3.1 BREAKDOWN FOR FIRST-ORDER SYSTEMS 63 3.2 BLOW-UP
OF SOLUTIONS TO THE EULER EQUATIONS 66 3.2.1 VORTEX SHEET BREAKDOWN AND
RAYLEIGH-TAYLOR INSTABILITY 70 3.2.2 A MATHEMATICAL THEORY FOR
SONOLUMINESCENCE 71 VIII CONTENTS 3.3 BLOW-UP OF SOLUTIONS TO THE
NAVIER-STOKES EQUATIONS 74 3.3.1 SELF-SIMILAR SOLUTIONS 77 3.3.2
BENARD-MARANGONI CONVECTION 78 4. CATASTROPHIC BEHAVIOUR IN OTHER
NON-LINEAR FLUID THEORIES 81 4.1 NON-EXISTENCE ON UNBOUNDED DOMAINS 81
4.1.1 LADYZHENSKAYA S MODELS 81 4.1.2 GLOBAL NON-EXISTENCE BACKWARD IN
TIME FOR MODEL I, WHEN THE SPATIAL DOMAIN IS R 2 86 4.1.3 GLOBAL
NON-EXISTENCE BACKWARD IN TIME FOR MODEL I, WHEN THE SPATIAL DOMAIN IS R
3 90 4.1.4 EXPONENTIAL GROWTH FOR MODEL II, BACKWARD IN TIME 94 4.1.5
THE BACKWARD IN TIME PROBLEM FOR MODEL III 97 4.2 A MODEL FOR A SECOND
GRADE FLUID IN GLACIER PHYSICS 99 4.2.1 NON-EXISTENCE FORWARD IN TIME
FOR MODEL I 101 4.2.2 NON-EXISTENCE BACKWARD IN TIME FOR MODEL I 103
4.2.3 EXPONENTIAL GROWTH FORWARD IN TIME FOR MODEL II . . 105 4.2.4
EXPONENTIAL BOUNDEDNESS BACKWARD IN TIME FOR MODEL II 108 4.3 BLOW-UP
FOR GENERALISED KDEV EQUATIONS 108 4.4 VERY RAPID GROWTH IN
FERROHYDRODYNAMICS 112 4.5 TEMPERATURE BLOW-UP IN AN ICE SHEET 115 5.
BLOW-UP IN VOLTERRA EQUATIONS 119 5.1 BLOW-UP FOR A SOLUTION TO A
VOLTERRA EQUATION 119 5.1.1 A GENERAL NON-LINEAR VOLTERRA EQUATION 122
5.1.2 VOLTERRA EQUATIONS MOTIVATED BY PARTIAL DIFFERENTIAL EQUATIONS ON
A BOUNDED SPATIAL DOMAIN 125 5.2 BLOW-UP FOR A SOLUTION TO A SYSTEM OF
VOLTERRA EQUATIONS . 126 5.2.1 COUPLED NON-LINEAR VOLTERRA EQUATIONS
WHICH MAY ARISE FROM NON-LINEAR PARABOLIC SYSTEMS 127 6. CHEMOTAXIS 131
6.1 MATHEMATICAL THEORIES OF CHEMOTAXIS 131 6.1.1 A SIMPLIFIED MODEL 133
6.2 BLOW-UP IN CHEMOTAXIS WHEN THERE ARE TWO DIFFUSION TERMS 134 6.3
BLOW-UP IN CHEMOTAXIS WITH A SINGLE DIFFUSION TERM 137 7. CHANGE OF TYPE
143 7.1 INSTABILITY IN A HYPOPLASTIC MATERIAL 143 CONTENTS IX 7.2
INSTABILITY IN A VISCOUS PLASTIC MODEL FOR SEA ICE DYNAMICS 150 7.3
PRESSURE DEPENDENT VISCOSITY FLOW 152 8. RAPID ENERGY GROWTH IN PARALLEL
FLOWS 155 8.1 RAPID GROWTH IN INCOMPRESSIBLE VISCOUS FLOWS 155 8.1.1
PARALLEL FLOWS 158 8.1.2 ENERGY GROWTH IN CIRCULAR PIPE FLOW 168 8.1.3
LINEAR INSTABILITY OF ELLIPTIC PIPE FLOW 171 8.2 TRANSIENT GROWTH IN
COMPRESSIBLE FLOWS 172 8.3 SHEAR FLOW IN GRANULAR MATERIALS 173 8.4
ENERGY GROWTH IN PARALLEL FLOWS OF SUPERIMPOSED VISCOUS FLUIDS 176
BIBLIOGRAPHY 179 SUBJECT INDEX 193
|
| any_adam_object | 1 |
| author | Straughan, Brian 1947- |
| author_GND | (DE-588)115774688 |
| author_facet | Straughan, Brian 1947- |
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| building | Verbundindex |
| bvnumber | BV011767008 |
| callnumber-first | T - Technology |
| callnumber-label | TA350 |
| callnumber-raw | TA350 |
| callnumber-search | TA350 |
| callnumber-sort | TA 3350 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | SK 540 UF 1500 |
| classification_tum | PHY 200f MTA 309f PHY 013f |
| ctrlnum | (OCoLC)37890525 (DE-599)BVBBV011767008 |
| dewey-full | 532/.051/01515353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.051/01515353 |
| dewey-search | 532/.051/01515353 |
| dewey-sort | 3532 251 71515353 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:15:24Z |
| institution | BVB |
| isbn | 3540635890 |
| language | German |
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| physical | IX, 196 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| spelling | Straughan, Brian 1947- Verfasser (DE-588)115774688 aut Explosive instabilities in mechanics Brian Straughan Berlin [u.a.] Springer 1998 IX, 196 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Blowing up (Algebraic geometry) Mechanics, Applied Mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Blowing up (DE-588)4508027-6 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Blowing up (DE-588)4508027-6 s Mechanik (DE-588)4038168-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007940570&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Straughan, Brian 1947- Explosive instabilities in mechanics Mathematik Blowing up (Algebraic geometry) Mechanics, Applied Mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd Blowing up (DE-588)4508027-6 gnd Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4508027-6 (DE-588)4038168-7 |
| title | Explosive instabilities in mechanics |
| title_auth | Explosive instabilities in mechanics |
| title_exact_search | Explosive instabilities in mechanics |
| title_full | Explosive instabilities in mechanics Brian Straughan |
| title_fullStr | Explosive instabilities in mechanics Brian Straughan |
| title_full_unstemmed | Explosive instabilities in mechanics Brian Straughan |
| title_short | Explosive instabilities in mechanics |
| title_sort | explosive instabilities in mechanics |
| topic | Mathematik Blowing up (Algebraic geometry) Mechanics, Applied Mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd Blowing up (DE-588)4508027-6 gnd Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Mathematik Blowing up (Algebraic geometry) Mechanics, Applied Mathematics Partielle Differentialgleichung Blowing up Mechanik |
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