Self-similarity and beyond: exact solutions of nonlinear problems
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall CRC
2000
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| Series: | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics
113 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 319 S. graph. Darst. |
| ISBN: | 1584882115 |
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Record in the Search Index
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| adam_text | TZ CHAPMAN & HALL/CRC MONOGRAPHS AND SURVEYS IN PURE AND APPLIED
MATHEMATICS I I 3 SELF-SIMILARITY AND BEYOND EXACT SOLUTIONS OF
NONLINEAR PROBLEMS P. L SACHDEV CHAPMAN & HALL/CRC BOCA RATON LONDON NEW
YORK WASHINGTON, D.C. CONTENTS 1 INTRODUCTION 1 2 FIRST-ORDER PARTIAL
DIFFERENTIAL EQUATIONS 5 2.1 LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF
FIRST ORDER 5 2.2 QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS OF FIRST
ORDER . . 9 2.3 REDUCTION OF U T + U N U X + H(X, T, U) = 0 27 2.4
INITIAL VALUE PROBLEM FOR U T + G(U)U X + XH(U) = 0 32 2.5 INITIAL VALUE
PROBLEM FOR U T + U A U X + XU 0 =0 41 3 EXACT SIMILARITY SOLUTIONS OF
NONLINEAR PDES 51 PART A 51 3.1 REDUCTION OF PDES BY INFINITESIMAL
TRANSFORMATIONS . . . . 51 3.2 SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS
63 3.3 SELF-SIMILAR SOLUTIONS OF THE SECOND KIND - VISCOUS GRAVITY
CURRENTS 73 PART B 85 3.4 INTRODUCTION 85 3.5 A NONLINEAR HEAT EQUATION
IN THREE DIMENSIONS 85 3.6 SIMILARITY SOLUTION OF BURGERS EQUATION BY
THE DIRECT METHOD 88 3.7 EXACT FREE SURFACE FLOWS FOR SHALLOW-WATER
EQUATIONS VIA THE DIRECT SIMILARITY APPROACH 97 3.8 MULTFPRONGED
APPROACH TO EXACT SOLUTIONS OF NONLINEAR PDES - AN EXAMPLE FROM
GASDYNAMICS 106 4 EXACT TRAVELLING WAVE SOLUTIONS 127 4.1 TRAVELLING
WAVE SOLUTIONS 127 4.2 SIMPLE WAVES IN 1-D GASDYNAMICS 128 4.3
ELEMENTARY NONLINEAR DIFFUSIVE TRAVELLING WAVES 131 4.4 TRAVELLING WAVES
FOR HIGHER-ORDER DIFFUSIVE SYSTEMS . . . . 142 VII VIII CONTENTS 4.5
SIMPLE WAVE FLOWS IN MULTIDIMENSIONAL SYSTEMS OF HOMO- GENEOUS PARTIAL
DIFFERENTIAL EQUATIONS 148 4.6 TRAVELLING WAVES FOR NONHOMOGENEOUS
HYPERBOLIC OR DISPER- SIVE SYSTEMS 154 4.7 EXACT HYDROMAGNETIC
TRAVELLING WAVES 161 4.8 EXACT SIMPLE WAVES ON SHEAR FLOWS IN A
COMPRESSIBLE BAROTROPIC MEDIUM 167 5 EXACT LINEARISATION OF NONLINEAR
PDES 175 5.1 INTRODUCTION 175 5.2 COMMENTS ON THE SOLUTION OF LINEAR
PDES 176 5.3 BURGERS EQUATION IN ONE AND HIGHER DIMENSIONS 178 5.4
NONLINEAR DEGENERATE DIFFUSION EQUATION U T = [FI^U 1 ^ . 182 5.5
ONE-DIMENSIONAL MOTION OF AN IDEAL COMPRESSIBLE ISENTROPIC GAS IN THE
HODOGRAPH PLANE 185 5.6 THE BORN-INFELD EQUATION 190 5.7 WATER WAVES UP
A UNIFORMLY SLOPING BEACH 193 5.8 SIMPLE WAVES ON SHEAR FLOWS 201 5.9
C-INTEGRABLE NONLINEAR PDES 206 6 NONLINEARISATION AND EMBEDDING OF
SPECIAL SOLUTIONS 213 6.1 INTRODUCTION 213 6.2 EXACT NONLINEARISATION OF
N WAVE SOLUTIONS FOR GENERALISED BURGERS EQUATIONS 216 6.3 BURGERS
EQUATION IN CYLINDRICAL COORDINATES WITH AXISYM- METRY 225 6.4 NONPLANAR
BURGERS EQUATION - A COMPOSITE SOLUTION . . . 228 6.5 MODIFIED BURGERS
EQUATION 239 6.6 EMBEDDING OF SIMILARITY SOLUTION IN A LARGER CLASS 245
7 ASYMPTOTIC SOLUTIONS BY BALANCING ARGUMENTS 257 7.1 ASYMPTOTIC
SOLUTION BY BALANCING ARGUMENTS - EXAMPLES FROM ODES 257 7.2
ASYMPTOTIC SOLUTION OF NONPLANAR BURGERS EQUATION WITH N WAVE INITIAL
CONDITIONS 263 7.3 ASYMPTOTIC PROFILES WITH FINITE MASS IN 1-D
CONTAMINANT TRANSPORT THROUGH POROUS MEDIA 268 8 SERIES SOLUTIONS OF
NONLINEAR PDES 285 8.1 INTRODUCTION 285 8.2 ANALYSIS OF EXPANSION OF A
GAS SPHERE (CYLINDER) INTO VACUUM286 8.3 COLLAPSE OF A SPHERICAL OR
CYLINDRICAL CAVITY 292 8.4 CONVERGING SHOCK WAVE FROM A SPHERICAL OR
CYLINDRICAL PISTON297
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:44:49Z |
| institution | BVB |
| isbn | 1584882115 |
| language | English |
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| physical | IX, 319 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Chapman & Hall CRC |
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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 | Sachdev, P. L. Verfasser aut Self-similarity and beyond exact solutions of nonlinear problems P. L. Sachdev Boca Raton [u.a.] Chapman & Hall CRC 2000 IX, 319 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC monographs and surveys in pure and applied mathematics 113 Differential equations, Nonlinear Numerical solutions Exakte Lösung (DE-588)4348289-2 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Exakte Lösung (DE-588)4348289-2 s DE-604 Chapman & Hall/CRC monographs and surveys in pure and applied mathematics 113 (DE-604)BV013350872 113 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009126811&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sachdev, P. L. Self-similarity and beyond exact solutions of nonlinear problems Chapman & Hall/CRC monographs and surveys in pure and applied mathematics Differential equations, Nonlinear Numerical solutions Exakte Lösung (DE-588)4348289-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4348289-2 (DE-588)4128900-6 |
| title | Self-similarity and beyond exact solutions of nonlinear problems |
| title_auth | Self-similarity and beyond exact solutions of nonlinear problems |
| title_exact_search | Self-similarity and beyond exact solutions of nonlinear problems |
| title_full | Self-similarity and beyond exact solutions of nonlinear problems P. L. Sachdev |
| title_fullStr | Self-similarity and beyond exact solutions of nonlinear problems P. L. Sachdev |
| title_full_unstemmed | Self-similarity and beyond exact solutions of nonlinear problems P. L. Sachdev |
| title_short | Self-similarity and beyond |
| title_sort | self similarity and beyond exact solutions of nonlinear problems |
| title_sub | exact solutions of nonlinear problems |
| topic | Differential equations, Nonlinear Numerical solutions Exakte Lösung (DE-588)4348289-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Differential equations, Nonlinear Numerical solutions Exakte Lösung Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009126811&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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