Theory and applications of partial differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Plenum Press
1997
|
| Schriftenreihe: | Mathematical concepts and methods in science and engineering
46 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 439 S. graph. Darst. |
| ISBN: | 0306456400 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | THEORY AND APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS PIERO
BASSANINI UNIVERSITY OF ROME LA SAPIENZA ROME, ITALY AND ALAN R.
ELCRAT WICHITA STATE UNIVERSITY WICHITA, KANSAS PLENUM PRESS * NEW YORK
AND LONDON CONTENTS 1. INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS 1
1. POPULATION DIFFUSION 2 2. VIBRATING STRING EQUATION 4 3. EQUATIONS
FOR ISENTROPIC FLOW OF A PERFECT GAS 5 4. CLASSIFICATION AND
CHARACTERISTICS 7 EXERCISES 8 REFERENCES 9 2. WAVE EQUATION 11 1.
INITIAL VALUE PROBLEM 11 2. INITIAL-BOUNDARY VALUE PROBLEMS 16 3.
REFLECTION PROBLEM 24 4. LINEAR HYPERBOLIC SYSTEMS WITH CONSTANT
COEFFICIENTS IN TWO VARIABLES 29 5. WAVE EQUATION IN TWO AND THREE
DIMENSIONS 32 EXERCISES 43 REFERENCES 51 3. HEAT EQUATION 53 1. HEAT
KERNEL AND MISCELLANEOUS SOLUTIONS 53 2. MAXIMUM PRINCIPLE 64 3. INITIAL
VALUE PROBLEM 71 4. INHOMOGENEOUS INITIAL VALUE PROBLEM 82 5.
INITIAL-BOUNDARY VALUE PROBLEMS 88 EXERCISES 96 REFERENCES 101 4.
LAPLACE EQUATION 10 3 1. POTENTIAL THEORY: BASIC NOTIONS. , 104 2.
GENERAL PROPERTIES OF HARMONIC FUNCTIONS 109 2.1. GREEN S IDENTITIES 109
VIII CONTENTS 2.2. MAXIMUM PRINCIPLE 112 2.3. GREEN S FUNCTION,
POISSON S INTEGRAL, AND MEAN VALUE THEOREM 115 2.4. OTHER CONSEQUENCES
OF THE POISSON FORMULA AND THE MEAN VALUE PROPERTY 119 2.5. VOLUME
POTENTIAL AND POISSON S EQUATION 126 3. DIRICHLET PROBLEM 129 3.1.
PERRON S METHOD 129 3.2. C 1 REGULARITY UP TO THE BOUNDARY 137 4.
INTEGRAL EQUATION FORMULATIONS OF DIRICHLET AND NEUMANN PROBLEMS 145
4.1. INTEGRAL OPERATORS WITH WEAKLY SINGULAR KERNEL 146 4.2. LAYER
POTENTIALS 150 4.3. LAYER ANSATZ AND BOUNDARY INTEGRAL EQUATIONS 156
4.4. DIRECT METHOD 160 4.5. POINCARE S IDENTITY AND HARMONIC VECTOR
FIELDS 162 5. VARIATIONAL THEORY 165 5.1. VARIATIONAL SOLUTIONS OF
DIRICHLET S PROBLEM 166 5.2. VARIATIONAL THEORY FOR POISSON S EQUATION
171 5.3. LAPLACE-DIRICHLET EIGENVALUE PROBLEM 173 6. CAPACITY 178 7.
APPLICATIONS 189 7.1. A PROBLEM CONCERNING ASYMPTOTIC EFFICIENCY OF
COOLING (CRUSHED ICE) 189 7.2. A FREE BOUNDARY PROBLEM MODELING
SEPARATED HOW OF AN INCOMPRESSIBLE FLUID 194 APPENDIX TO SECTION 1 198
EXERCISES 201 REFERENCES 211 5. ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
OF SECOND ORDER 21 3 1. MAXIMUM PRINCIPLE 213 2. APPLICATIONS OF THE
MAXIMUM PRINCIPLE 219 3. EQUATIONS WITH DISCONTINUOUS COEFFICIENTS 226
4. NONLINEAR ELLIPTIC EQUATIONS 237 4.1. MONOTONE OPERATORS 237 4.2.
DIRICHLET PROBLEM FOR THE MINIMAL SURFACE EQUATION 242 EXERCISES 259
REFERENCES 266 CONTENTS IX 6. ABSTRACT EVOLUTION EQUATIONS 269 1.
SOLUTION OF THE HEAT EQUATION BY EIGENFUNCTION EXPANSIONS 270 2.
PARABOLIC EVOLUTION EQUATIONS 273 3. NONLINEAR INITIAL VALUE PROBLEM 281
EXERCISES 287 REFERENCES 289 7. HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
IN ONE SPACE VARIABLE 291 1. INTRODUCTION 291 2. LOCAL EXISTENCE THEOREM
FOR A.E. AND SMOOTH SOLUTIONS OF THE CAUCHY PROBLEM 300 3. SCALAR
EQUATIONS 318 3.1. WEAK SOLUTIONS 320 3.2. KRUZHKOV S THEOREM 327 3.3.
RIEMANN PROBLEM 342 3.4. WAVE INTERACTION 346 4. SYSTEMS IN ONE SPACE
VARIABLE 350 4.1. ENTROPY CONDITIONS 352 4.2. RIEMANN PROBLEM 354 5.
PROOF OF EXISTENCE FOR WEAK SOLUTIONS OF SYSTEMS OF CONSERVATION LAWS
363 APPENDIX TO SECTION 5 382 EXERCISES 388 REFERENCES 392 8.
DISTRIBUTIONS AND SOBOLEV SPACES 395 1. BANACH AND HILBERT SPACES 395 2.
THEORY OF DISTRIBUTIONS 403 3. SOBOLEV SPACES 411 4. VECTOR-VALUED
FUNCTIONS 421 EXERCISES 427 REFERENCES 434 INDEX 437
|
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| id | DE-604.BV011935027 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:18:47Z |
| institution | BVB |
| isbn | 0306456400 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008067259 |
| oclc_num | 37725528 |
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| physical | IX, 439 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Plenum Press |
| record_format | marc |
| series | Mathematical concepts and methods in science and engineering |
| series2 | Mathematical concepts and methods in science and engineering |
| spelling | Bassanini, Piero Verfasser aut Theory and applications of partial differential equations Piero Bassanini and Alan R. Elcrat New York [u.a.] Plenum Press 1997 IX, 439 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical concepts and methods in science and engineering 46 Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Elcrat, Alan R. Verfasser aut Mathematical concepts and methods in science and engineering 46 (DE-604)BV000001144 46 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008067259&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bassanini, Piero Elcrat, Alan R. Theory and applications of partial differential equations Mathematical concepts and methods in science and engineering Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Theory and applications of partial differential equations |
| title_auth | Theory and applications of partial differential equations |
| title_exact_search | Theory and applications of partial differential equations |
| title_full | Theory and applications of partial differential equations Piero Bassanini and Alan R. Elcrat |
| title_fullStr | Theory and applications of partial differential equations Piero Bassanini and Alan R. Elcrat |
| title_full_unstemmed | Theory and applications of partial differential equations Piero Bassanini and Alan R. Elcrat |
| title_short | Theory and applications of partial differential equations |
| title_sort | theory and applications of partial differential equations |
| topic | Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differential equations, Partial Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008067259&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001144 |
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