Nonlinear hyperbolic waves in multidimensions:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2001
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| Series: | Chapman & Hall CRC monographs and surveys in pure and applied mathematics
121 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 338 S. graph. Darst. |
| ISBN: | 1584880724 |
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| adam_text | K CHAPMAN & HALL/CRC MONOGRAPHS AND SURVEYS IN PURE AND APPLIED
MATHEMATICS 121 NONLINEAR HYPERBOLIC WAVES IN MULTI-DIMENSIONS PHOOLAN
PRASAD CHAPMAN & HALL/CRC BOCA RATON LONDON NEW YORK WASHINGTON, D.C.
NONLINEAR HYPERBOLIC WAVES IN MULTI-DIMENSIONS PHOOLAN PRASAD CONTENTS
CHAPTER 1 1 AN INTRODUCTION TO NONLINEAR HYPERBOLIC WAVES 1 1.1 A WAVE
EQUATION WITH GENUINE NONLINEARITY 1 1.2 BREAKDOWN OF A GENUINE SOLUTION
4 1.3 CONSERVATION LAW AND JUMP CONDITION 7 1.4 STABILITY CONSIDERATION,
ENTROPY CONDITION AND 10 SHOCKS 1.5 SOME EXAMPLES 16 1.6 SHOCK
STRUCTURE, DISSIPATION AND ENTROPY 26 CONDITION 1.7 THE PERSISTENCE OF A
SHOCK 33 1.8 NONLINEAR WAVEFRONT AND SHOCK FRONT 36 1.9 HOPF S RESULT ON
THE GENERAL SOLUTION 39 1.10 EQUAL AREA RULE FOR SHOCK FITTING 41
CHAPTER 2 2 HYPERBOLIC SYSTEM - SOME BASIC RESULTS 47 2.1 HYPERBOLIC
SYSTEM OF FIRST ORDER EQUATIONS 47 IN TWO INDEPENDENT VARIABLES 2.1.1
DEFINITION OF A HYPERBOLIC SYSTEM 47 2.1.2 A CANONICAL FORM OF A SYSTEM
OF LINEAR 50 AND SEMILINEAR EQUATIONS 2.2 THE WAVE EQUATION IN M( 1)
SPACE DIMENSIONS 53 2.2.1 SPACE-LIKE SURFACE AND TIME-LIKE DIRECTION
54 2.2.2 BICHARACTERISTICS AND RAYS 56 2.2.3 COMPATIBILITY CONDITION ON
A CHARACTERISTIC 58 SURFACE XI 2.2.4 PROPAGATION OF DISCONTINUITIES IN
SECOND 60 ORDER DERIVATIVES ALONG RAYS 2.3 HYPERBOLIC SYSTEM IN MORE
THAN TWO 62 INDEPENDENT VARIABLES 2.3.1 SPACE-LIKE SURFACE AND TIME-LIKE
DIRECTION 63 2.3.2 EXPLICIT DEFINITION OF A HYPERBOLIC SYSTEM 67 2.4
BICHARACTERISTIC CURVES, RAYS AND COMPATIBILITY 69 CONDITION 2.5
PROPAGATION OF DISCONTINUITIES OF FIRST ORDER 74 DERIVATIVES ALONG RAYS
CHAPTER 3 3 SIMPLE WAVE, HIGH FREQUENCY 77 APPROXIMATION AND RAY THEORY
3.1 SIMPLE WAVE 77 3.1.1 EXAMPLE OF A SIMPLE WAVE IN GAS DYNAMICS 78
3.1.2 SIMPLE WAVE IN ONE SPACE DIMENSION 84 3.1.3 SIMPLE WAVE IN
MULTI-DIMENSIONS 90 3.1.4 AN INITIAL VALUE PROBLEM LEADING TO A 94 KTH
SIMPLE WAVE 3.2 HIGH-FREQUENCY APPROXIMATION, WAVEFRONT, 96 HUYGENS
METHOD AND FERMAT S PRINCIPLE 3.2.1 DEFINITION OF A WAVEFRONT 96 3.2.2
HUYGENS METHOD OF WAVEFRONT CONSTRUCTION 98 3.2.3 HUYGENS METHOD AND
RAY THEORY 102 3.2.4 FERMAT S PRINCIPLE 104 3.2.5 FERMAT S PRINCIPLE IN
A STATIONARY MEDIUM 106 3.2.6 FERMAT S PRINCIPLE IN A NONSTATIONARY
MEDIUM 108 3.2.7 WEAKLY NONLINEAR RAY THEORY (WNLRT) IN AN 110 ISOTROPIC
MEDIUM USING FERMAT S PRINCIPLE 3.3 KINEMATICS OF A PROPAGATING CURVE
112 3.3.1 CAUSTIC, WAVEFRONT FOLDING AND SOME 112 OTHER GENERAL
PROPERTIES 3.3.2 RAY COORDINATE SYSTEM AND KINEMATICAL 117 CONSERVATION
LAWS 3.3.3 TWO TYPES OF SINGULARITIES AND JUMP 121 CONDITIONS ACROSS A
KINK XN 3.3.4 KINEMATICAL COMPATIBILITY CONDITIONS ON 128 A SURFACE OF
DISCONTINUITY IN MULTI-DIMENSIONS 3.4 BREAKDOWN OF THE CONTINUITY OF A
SOLUTION 128 OF A QUASILINEAR SYSTEM 3.4.1 COMBINED EFFECT OF GENUINE
NONLINEARITY AND 129 GEOMETRICAL DIVERGENCE 3.4.2 TRANSPORT EQUATION FOR
DISCONTINUITIES IN 133 DERIVATIVES FOR A SYSTEM IN MULTI-DIMENSIONS 3.5
JUMP CONDITIONS ON A CURVED SHOCK 137 CHAPTER 4 4 4.1 4.2 4.3 4.3.1
4.3.2 4.4 4.4.1 4.4.2 4.4.3 WEAKLY NONLINEAR RAY THEORY (WNLRT):
DERIVATION A HISTORICAL ACCOUNT DERIVATION OF CPW THEORY A GEOMETRIC
DERIVATION OF WNLRT WNLRT FOR A HYPERBOLIC SYSTEM UPSTREAM PROPAGATING
WAVES IN A STEADY FLOW OF A POLYTROPIC GAS AN ASYMPTOTIC DERIVATION OF
WNLRT DERIVATION OF EIKONAL AND TRANSPORT EQUATIONS RAY FORMULATION OF
THE ASYMPTOTIC EQUATIONS COMPARISON WITH OTHER THEORIES CHAPTER 5 5 5.1
5.2 5.2.1 5.2.2 5.3 STABILITY OF SOLUTIONS NEAR A SINGULARITY OF SONIC
TYPE INTRODUCTION ONE-DIMENSIONAL WEAKLY NONLINEAR WAVE PROPAGATION BKPS
THEORY SONIC TYPE OF SINGULARITY IN SELF-SIMILAR SOLUTIONS WAVES IN A
MULTI-DIMENSIONAL STEADY TRANSONIC FLOW 143 143 146 149 150 156 158 158
163 168 173 173 178 180 188 195 XM CHAPTER 6 6 WNLRT IN A POLYTROPIC GAS
205 6.1 BASIC EQUATIONS 205 6.1.1 NON-DIMENSIONAL FORM OF EQUATIONS OF
WNLRT 207 IN TWO-SPACE-DIMENSIONS 6.1.2 A SIMPLE WAVE SOLUTION 211 6.2
GEOMETRICAL FEATURES OF A NONLINEAR WAVEFRONT 213 6.2.1 ELEMENTARY WAVE
SOLUTIONS AND THEIR 214 INTERPRETATION AS ELEMENTARY SHAPES 6.2.2
SOLUTION OF THE RIEMANN PROBLEM AND 217 INTERPRETATION 6.2.3 INTERACTION
OF ELEMENTARY SHAPES 220 6.3 EXACT SOLUTION OF AN INITIAL VALUE PROBLEM
222 6.4 CONCLUSION AND VALIDITY OF WNLRT 226 CHAPTER 7 7 COMPATIBILITY
CONDITIONS ON A SHOCK: 229 SINGLE CONSERVATION LAW 7.1 DERIVATION OF THE
INFINITE SYSTEM OF 229 COMPATIBILITY CONDITIONS 7.2 EXISTENCE AND
UNIQUENESS OF THE SOLUTION OF THE 233 INFINITE SYSTEM 7.3 A NEW THEORY
OF SHOCK DYNAMICS: ANALYTIC 236 CONSIDERATIONS 7.4 A NEW THEORY OF SHOCK
DYNAMICS: COMPARISON 239 OF NUMERICAL RESULTS WITH THE EXACT SOLUTION
7.5 CONCLUSION 245 CHAPTER 8 8 ONE-DIMENSIONAL PISTON PROBLEM: AN 247
APPLICATION OF NTSD 8.1 FORMULATION OF THE PROBLEM 248 8.2 DYNAMICAL
COMPATIBILITY CONDITIONS 249 8.3 INITIAL CONDITIONS FOR THE PISTON
PROBLEM 255 8.4 RESULTS AND DISCUSSIONS 257 XIV CHAPTER 9 9
COMPATIBILITY CONDITIONS ON A SHOCK 265 MANIFOLD IN MULTI-DIMENSIONS 9.1
SHOCK RAYS 265 9.2 SHOCK MANIFOLD EQUATION FOR A WEAK SHOCK 266 9.3
GEOMETRICAL AND KINEMATICAL COMPATIBILITY 268 CONDITIONS 9.3.1
PRELIMINARY GEOMETRICAL IDEAS FOR A MOVING 268 CURVE IN
TWO-SPACE-DIMENSIONS 9.3.2 GEOMETRICAL COMPATIBILITY CONDITIONS 270
9.3.3 SOME RESULTS IN A RAY COORDINATE SYSTEM 272 9.3.4 KINEMATICAL
COMPATIBILITY CONDITIONS 273 9.4 DYNAMICAL COMPATIBILITY CONDITIONS 273
9.4.1 THE FIRST SET OF DYNAMICAL COMPATIBILITY 275 CONDITIONS 9.4.2 THE
SECOND SET OF DYNAMICAL COMPATIBILITY 278 CONDITIONS 9.4.3 FIRST AND
SECOND SET OF EQUATIONS IN THE 284 SHOCK RAY THEORY 9.5 A WEAK SHOCK RAY
THEORY 286 CHAPTER 10 10 PROPAGATION OF A CURVED WEAK SHOCK 289 10.1
GOVERNING EQUATIONS OF THE NTSD 289 10.2 CONSERVATION FORM OF THE
EQUATIONS FOR A 293 TWO-DIMENSIONAL SHOCK PROPAGATION 10.3 INITIAL
CONDITIONS, RESULTS AND DISCUSSION 297 10.3.1 PROPAGATION OF A SHOCK
FRONT INITIALLY 298 PARABOLIC IN SHAPE 10.3.2 PROPAGATION OF A SHOCK
FRONT WITH INITIALLY 305 SINUSOIDAL SHAPE AND PERIODIC AMPLITUDE
DISTRIBUTION 10.3.3 PROPAGATION OF SHOCK FRONT WITH INITIALLY 308
ASYMMETRIC BUT PIECEWISE PARABOLIC SHAPE IN EACH PERIOD XV 10.3.4
PROPAGATION OF A SHOCK FRONT WITH INITIALLY 310 PERIODIC BUT ARBITRARY
SHAPE IN EACH PERIOD 10.3.5 WHEN THE INITIAL SHOCK FRONT HAS A SINGLE
311 SMOOTH DENT OR BULGE 10.4 COMPARISON WITH OTHER THEORIES 315 10.4.1
QUALITATIVE VERIFICATION OF THE SHAPE OF THE 315 FRONT OBTAINED BY DNS
TO SUPPORT THE KINK THEORY 10.4.2 COMPARISON WITH EARLIER THEORIES 315
10.4.3 COMPARISON WITH WEAKLY NONLINEAR RAY THEORY 318 10.4.4 COMPARISON
WITH WHITHAM S THEORY 319 10.5 CORRUGATIONAL STABILITY AND
PERSISTENCE..OF 322 A KINK REFERENCES 325 INDEX 337 XVI
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| institution | BVB |
| isbn | 1584880724 |
| language | English |
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| physical | 338 S. graph. Darst. |
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| series | Chapman & Hall CRC monographs and surveys in pure and applied mathematics |
| series2 | Chapman & Hall CRC monographs and surveys in pure and applied mathematics |
| spelling | Prasad, Phoolan Verfasser aut Nonlinear hyperbolic waves in multidimensions Phoolan Prasad Boca Raton [u.a.] CRC Press 2001 338 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC monographs and surveys in pure and applied mathematics 121 Nichtlineare Wellengleichung (DE-588)4042104-1 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Nichtlineare Wellengleichung (DE-588)4042104-1 s Hyperbolische Differentialgleichung (DE-588)4131213-2 s DE-604 Chapman & Hall CRC monographs and surveys in pure and applied mathematics 121 (DE-604)BV013350872 121 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010500564&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prasad, Phoolan Nonlinear hyperbolic waves in multidimensions Chapman & Hall CRC monographs and surveys in pure and applied mathematics Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| subject_GND | (DE-588)4042104-1 (DE-588)4131213-2 |
| title | Nonlinear hyperbolic waves in multidimensions |
| title_auth | Nonlinear hyperbolic waves in multidimensions |
| title_exact_search | Nonlinear hyperbolic waves in multidimensions |
| title_full | Nonlinear hyperbolic waves in multidimensions Phoolan Prasad |
| title_fullStr | Nonlinear hyperbolic waves in multidimensions Phoolan Prasad |
| title_full_unstemmed | Nonlinear hyperbolic waves in multidimensions Phoolan Prasad |
| title_short | Nonlinear hyperbolic waves in multidimensions |
| title_sort | nonlinear hyperbolic waves in multidimensions |
| topic | Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| topic_facet | Nichtlineare Wellengleichung Hyperbolische Differentialgleichung |
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