Mathematical analysis and numerical methods for science and technology: 1 Physical origins and classical methods
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| Format: | Book |
| Language: | English French |
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Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London
Springer-Verlag
2000
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| Edition: | [Nachdr.] |
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 719 S. |
| ISBN: | 3540660976 |
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MARC
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| 240 | 1 | 0 | |a Analyse mathématique et calcul numérique pour les sciences et les techniques |
| 245 | 1 | 0 | |a Mathematical analysis and numerical methods for science and technology |n 1 |p Physical origins and classical methods |c Robert Dautray ; Jacques-Louis Lions |
| 250 | |a [Nachdr.] | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London |b Springer-Verlag |c 2000 | |
| 300 | |a XVII, 719 S. | ||
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| 650 | 7 | |a Analyse mathématique |2 ram | |
| 650 | 7 | |a Analyse numérique |2 ram | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 700 | 1 | |a Lions, Jacques-Louis |d 1928-2001 |0 (DE-588)124055397 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008789641 | ||
Record in the Search Index
| _version_ | 1804127599847276544 |
|---|---|
| adam_text | Table
of Contents
Chapter I. Physical Examples
Introduction
.......................... 1
Part A
.
The Physical Models
................... 2
§1.
Classical Fluids and the Navier-Stokes System
......... 2
1.
Introduction: Mechanical Origin
.............. 2
2.
Corresponding Mathematical Problem
............ 5
3.
Linearisation. Stokes Equations
.............. 7
4.
Case of a Perfect Fluid. Euler s Equations
.......... 7
5.
Case of Stationary Flows. Examples of Linear Problems
.... 9
6.
Non-Stationary Flows Leading to the Equations of Viscous
Diffusion
........................ 15
7.
Conduction of Heat. Linear Example in the Mechanics of Fluids
18
8.
Example of Acoustic Propagation
.............. 23
9.
Example with Boundary Conditions on Oblique Derivatives
. . 25
Review
.......................... 27
§2.
Linear Elasticity
...................... 28
1.
Introduction: Elasticity; Hyperelasticity
........... 28
2.
Linear (not Necessarily
Isotropie)
Elasticity
......... 29
3. Isotropie
Linear Elasticity (or Classical Elasticity)
....... 32
4.
Stationary Problems in Classical Elasticity
.......... 33
5.
Dynamical Problems in Classical Elasticity
.......... 37
6.
Problems of Thermal Diffusion. Classical Thermoelasticity
... 47
Review
.......................... 51
§3.
Linear Viscoelasticity
.................... 52
1.
Introduction
....................... 52
2.
Materials with Short Memory
............... 53
3.
Materials with Long Memory
............... 53
4.
Particular Case of
Isotropie
Media
............. 54
5.
Stationary Problems in Classical Viscoelasticity
........ 59
Review
.......................... 59
§4.
Electromagnetism
and Maxwell s Equations
.......... 59
1.
Fundamental Equations of
Electromagnetism
........ 59
2.
Macroscopic Equations:
Electromagnetism
in Continuous Media
65
XIV
Table of Contents
3.
Potentials. Gauge Transformation (Case of the Entire Space
R^xIR,)
........................ 80
4.
Some Evolution Problems
................. 83
5.
Static
Electromagnetism
.................. 87
6.
Stationary Problems
................... 91
Review
..........................
Ill
§5.
Neutronics. Equations of Transport and Diffusion
........ 113
1.
Problems of the Transport of Neutrons
........... 113
2.
Problems of Neutron Diffusion
.............. 117
3.
Stationary Problems
................... 121
Review
.......................... 126
§6.
Quantum Physics
...................... 128
Introduction
........................ 128
1.
The Fundamental Principles of Modelling
.......... 130
2.
Systems Consisting of One Particle
............. 142
3.
Systems of Several Particles
................ 152
Review
.......................... 157
Appendix. Concise Elements Concerning Some Mathematical Ideas
Used in this
§6....................... 157
Appendix Mechanics . Elements Concerning the Problems
of Mechanics
.......................... 162
§1.
Indiciai
Calculus. Elementary Techniques of the Tensor Calculus
. . 162
1.
Orientation Tensor or Fundamental Alternating Tensor in ]R3
. 162
2.
Possibilities of Decompositions of a Second Order Tensor
. . . 164
3.
Generalized Divergence Theorem
.............. 165
4.
Ideas About Wrenches
.................. 166
§2.
Notation, Language and Conventions in Mechanics
....... 167
1.
Lagrangian and Eulerian Coordinates
............ 167
2.
Notions of Displacement and of Strain
........... 168
3.
Notions of Velocity and of Rate of Strain
.......... 169
4.
Notions of Particle Derivative, of Acceleration and of Dilatation
170
5.
Notions of Trajectory and of Stream Line
.......... 171
§3.
ideas Concerning the Principle of Virtual Power
......... 172
1.
Introduction: Schematization of Forces
........... 172
2.
Preliminary Definitions
.................. 172
3.
Fundamental Statements
................. 175
4.
Theory of the First Gradient
................ 176
5.
Application to the Formulation of Curvilinear Media
..... 179
6.
Application to the Formulation of the Theory of Thin Plates
. . 183
Linear and Non-Linear Problems in
§1
to
§6
of this Chapter IA
. . . . 187
Table
of Contents XV
Part
В.
First Examination of the Mathematical Models
........ 191
§ 1.
The Principal Types of Linear Partial Differential Equations Seen
in Chapter IA
....................... 191
1.
Equation of Diffusion Type
................ 192
2.
Equation of the Type of Wave Equations
.......... 195
3. Schrödinger
Equation
................... 197
4.
The Equation
Аи
= ƒ
in which A is a Linear Operator not
Depending on the Time and
ƒ
is Given (Stationary Equations)
. 198
§2.
Global Constraints Imposed on the Solutions of a Problem: Inclu¬
sion in a Function Space; Boundary Conditions; Initial Conditions
. 201
1.
Introduction. Function Spaces
............... 201
2.
Initial Conditions and Evolution Problems
.......... 202
3.
Boundary Conditions
................... 204
4.
Transmission Conditions
................. 213
5.
Problems Involving Time-Derivatives of the Unknown Function
и
on the Boundary
..................... 215
6.
Problems of Time Delay
.................. 216
Review of Chapter IB
...................... 218
Chapter II. The Laplace Operator
Introduction
.......................... 220
§1.
The Laplace Operator
.................... 220
1.
Poisson s Equation
.................... 220
2.
Examples in Mechanics and Electrostatics
.......... 224
3.
Green s Formulae: The Classical Framework
......... 226
4.
The Laplacian in Polar Coordinates
............. 231
§2.
Harmonic Functions
.................... 236
1.
Definitions. Examples. Elementary Solutions
......... 236
2.
Gauss Theorem. Formulae of the Mean. The Maximum
Principle
........................ 243
3.
Poisson s Integral Formula; Regularity of Harmonic Functions;
Harnack s Inequality
................... 248
4.
Characterisation of Harmonic Functions. Elimination of
Singularities
....................... 255
5.
Kelvin s Transformation; Application to Harmonic Functions
in an Unbounded Set;
Conformai
Transformation
....... 264
6.
Some Physical Interpretations (in Mechanics and Electrostatics)
. 271
§3.
Newtonian Potentials
.................... 275
1.
Generalities on the Newtonian Potentials of a Distribution with
Compact Support
.................... 275
2.
Study of Local Regularity of Solutions of Poisson s Equation
. . 283
XVI Table of
Contents
3.
Regularity of Simple and Double Layer Potentials
...... 296
4.
Newtonian Potential of a Distribution Without Compact Support
307
5.
Some Physical Interpretations (in Mechanics and Electrostatics)
. 326
§4.
Classical Theory of Dirichlet s Problem
............ 328
1.
Generalities on Dirichlet s Problem
Ρ(Ω, φ)
in the Case
Ω
Bounded: Classical Solution, Examples, Outline of Perron s
Method, Generalized Solutions, Regular Point of the Boundary,
Barrier Function
..................... 328
2.
Generalities on the Dirichlet Problem
Ρ(Ω, φ,
f)
and the Green s
Function of
Ω,
a Bounded Open Set
............ 341
3.
Generalities on Dirichlet s Problem in an Unbounded Open Set
. 352
4.
The Neumann Problem; Mixed Problem;
Hopfs
Maximum
Principle; Examples
.................... 367
5.
Solution by Simple and Double Layer Potentials: Fredholm s
Integral Method
..................... 379
6.
Sub-Harmonic Functions. Perron s Method
......... 397
§5.
Capacities*
......................... 407
1.
Interior and Exterior Capacity Operators
.......... 407
2.
Electrical Equilibrium; Coefficients of Capacitance
...... 418
3.
Capacity of a Part of an Open Set in R
........... 433
§6.
Regularity*
......................... 457
1.
Regularity of the Solutions of Dirichlet and Neumann Problems
457
2.
Analytic Regularity and Trace on the Boundary of a Harmonic
Function
........................ 472
3.
Dirichlet Problem with Given Measures or Discontinuous
Functions. Herglotz s Theorem
............... 483
4.
Neumann Problem with Given Measures
.......... 497
5.
Dependence of Solutions of Dirichlet Problems as a Function
of the Open Set: Hadamard s Formula
........... 502
§7.
Other Methods of Solution of the Dirichlet Problem*
....... 507
1.
Case of a Convex Open Set: Neumann s Integral Method
. . . 507
2.
Alternating Procedure of
Schwarz ............. 515
3.
Method of Separation of Variables. Harmonic Polynomials.
Spherical Harmonic Function
............... 523
4.
Dirichlet s Method
.................... 542
5.
Symmetry Methods and Method of Images
......... 560
§8.
Elliptic Equations of the Second Order*
............ 568
1.
The Divergence Form, Green s Formula
........... 570
2.
Different Concepts of Solutions, Boundary Value Problems,
Transmission Conditions
................. 576
3.
General Results on the Regularity of Elliptic Problems of the
Second Order
...................... 585
Table
of Contents
XVII
4.
Results on Existence and Uniqueness of Solutions of Strictly
Elliptic Boundary Value Problems of the Second Order on a
Bounded Open Set
.................... 594
5.
Harnack s Inequality and the Maximum Principle
....... 607
6.
Green s Functions
.................... 624
7.
Helmholtz s Equation
................... 640
Review of Chapter II
...................... 658
Bibliography
.......................... 659
Table of Notations
....................... 667
Index
............................. 681
Contents of Volumes
2-6.................... 715
|
| any_adam_object | 1 |
| author | Dautray, Robert 1928- Lions, Jacques-Louis 1928-2001 |
| author_GND | (DE-588)133309347 (DE-588)124055397 |
| author_facet | Dautray, Robert 1928- Lions, Jacques-Louis 1928-2001 |
| author_role | aut aut |
| author_sort | Dautray, Robert 1928- |
| author_variant | r d rd j l l jll |
| building | Verbundindex |
| bvnumber | BV012912824 |
| ctrlnum | (OCoLC)44551963 (DE-599)BVBBV012912824 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | [Nachdr.] |
| format | Book |
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| id | DE-604.BV012912824 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:35:55Z |
| institution | BVB |
| isbn | 3540660976 |
| language | English French |
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| physical | XVII, 719 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Springer-Verlag |
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| spelling | Dautray, Robert 1928- (DE-588)133309347 aut Analyse mathématique et calcul numérique pour les sciences et les techniques Mathematical analysis and numerical methods for science and technology 1 Physical origins and classical methods Robert Dautray ; Jacques-Louis Lions [Nachdr.] Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London Springer-Verlag 2000 XVII, 719 S. txt rdacontent n rdamedia nc rdacarrier Analyse mathématique ram Analyse numérique ram Physique mathématique ram Lions, Jacques-Louis 1928-2001 (DE-588)124055397 aut (DE-604)BV013031479 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008789641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dautray, Robert 1928- Lions, Jacques-Louis 1928-2001 Mathematical analysis and numerical methods for science and technology Analyse mathématique ram Analyse numérique ram Physique mathématique ram |
| title | Mathematical analysis and numerical methods for science and technology |
| title_alt | Analyse mathématique et calcul numérique pour les sciences et les techniques |
| title_auth | Mathematical analysis and numerical methods for science and technology |
| title_exact_search | Mathematical analysis and numerical methods for science and technology |
| title_full | Mathematical analysis and numerical methods for science and technology 1 Physical origins and classical methods Robert Dautray ; Jacques-Louis Lions |
| title_fullStr | Mathematical analysis and numerical methods for science and technology 1 Physical origins and classical methods Robert Dautray ; Jacques-Louis Lions |
| title_full_unstemmed | Mathematical analysis and numerical methods for science and technology 1 Physical origins and classical methods Robert Dautray ; Jacques-Louis Lions |
| title_short | Mathematical analysis and numerical methods for science and technology |
| title_sort | mathematical analysis and numerical methods for science and technology physical origins and classical methods |
| topic | Analyse mathématique ram Analyse numérique ram Physique mathématique ram |
| topic_facet | Analyse mathématique Analyse numérique Physique mathématique |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008789641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013031479 |
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