Elements of partial differential equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2007
|
| Series: | de Gruyter textbook
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | IX, 245 S. graph. Darst. |
| ISBN: | 9783110191240 3110191245 |
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MARC
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| 245 | 1 | 0 | |a Elements of partial differential equations |c Pavel Drábek ; Gabriela Holubová |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2007 | |
| 300 | |a IX, 245 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text |
Contents
Preface
v
1
Mathematical Models, Conservation and Constitutive Laws
. 1
1.1
Basic Notions
. 1
1.2
Evolution Conservation Law
. 3
1.3
Stationary Conservation Law
. 4
1.4
Conservation Law in One Dimension
. 4
1.5
Constitutive Laws
. 6
1.6
Exercises
. 8
2
Classification, Types of Equations, Boundary and Initial Conditions
. 9
2.1
Basic Types of Equations, Boundary and Initial Conditions
. 9
2.2
Classification of Linear Equations of the Second Order
. 14
2.3
Exercises
. 17
3
Linear Partial Differential Equations of the First Order
. 21
3.1
Convection and Transport Equation
. 21
3.2
Equations with Constant Coefficients
. 22
3.3
Equations with Non-Constant Coefficients
. 28
3.4
Exercises
. 32
4
Wave Equation in One Spatial Variable
—
Cauchy Problem in
R
. 37
4.1
String Vibrations and Wave Equation in One Dimension
. 37
4.2
Cauchy Problem on the Real Line
. 40
4.3
Wave Equation with Sources
. 49
4.4
Exercises
. 53
5
Diffusion Equation in One Spatial Variable
—
Cauchy Problem in
IR
. 57
5.1
Diffusion and Heat Equations in One Dimension
. 57
5.2
Cauchy Problem on the Real Line
. 58
5.3
Diffusion Equation with Sources
. 65
5.4
Exercises
. 68
6
Laplace and
Poisson
Equations in Two Dimensions
. 71
6.1
Steady States and Laplace and
Poisson
Equations
. 71
6.2
Invariance
of the Laplace Operator, Its Transformation into Polar Co¬
ordinates
. 73
6.3
Solution of Laplace and
Poisson
Equations in R2
. 74
6.4
Exercises
. 76
vin
·
Contents
7
Solutions of Initial
Boundary Value Problems for Evolution Equations
. 78
7.1
Initial Boundary Value Problems on Half-Line
.78
7.2
Initial Boundary Value Problem on Finite Interval, Fourier Method
. 84
7.3
Fourier Method for Nonhomogeneous Problems
.99
7.4
Transformation to Simpler Problems
.103
7.5
Exercises
.104
8
Solutions of Boundary Value Problems for Stationary Equations
.113
8.1
Laplace Equation on Rectangle
.113
8.2
Laplace Equation on Disc
.115
8.3
Poisson
Formula
.117
8.4
Exercises
.119
9
Methods of Integral Transforms
.123
9.1
Laplace Transform
.123
9.2
Fourier Transform
.128
9.3
Exercises
.134
10
General Principles
.139
10.1
Principle of Causality (Wave Equation)
. 139
10.2
Energy Conservation Law (Wave Equation)
. 141
10.3
Ill-Posed Problem (Diffusion Equation for Negative t)
. 144
10.4
Maximum Principle (Heat Equation)
. 145
10.5
Energy Method (Diffusion Equation)
. 147
10.6
Maximum Principle (Laplace Equation)
. 148
10.7
Consequences of
Poisson
Formula (Laplace Equation)
. 150
10.8
Comparison of Wave, Diffusion and Laplace Equations
. 152
10.9
Exercises
. 152
11
Laplace and
Poisson
equations in Higher Dimensions
.157
11.1
Invariance
of the Laplace Operator
.157
11.2
Green's First Identity
.159
11.3
Properties of Harmonic Functions
.161
11.4
Green's Second Identity and Representation Formula
.164
11.5
Boundary Value Problems and Green's Function
.166
11.6
Dirichlet Problem on Half-Space and on Ball
.168
11.7
Exercises
.174
12
Diffusion Equation in Higher Dimensions
.178
12.1
Heat Equation in Three Dimensions
.178
12.2
Cauchy Problem in E3
.179
12.3
Diffusion on Bounded Domains, Fourier Method
.182
12.4
Exercises
.192
Contents_ jx
13
Wave Equation
in Higher
Dimensions
.I95
13.1 Membrane
Vibrations and Wave Equation
in
Two Dimensions
.
I95
13.2
Cauchy Problem in R3—
Kirchhoff
's
Formula
.196
13.3
Cauchy problem in
R2
.
I99
13.4
Wave with sources in
R3
.202
13.5
Characteristics, Singularities, Energy and Principle of Causality
. . . .204
13.6
Wave on Bounded Domains, Fourier Method
.208
13.7
Exercises
.224
14
Appendix
.228
14.1
Sturm-Liouville problem
.228
14.2
Bessel Functions
.229
Some Typical Problems Considered in This Book
.235
Notation
.237
Bibliography
.239
Index
.241 |
| adam_txt |
Contents
Preface
v
1
Mathematical Models, Conservation and Constitutive Laws
. 1
1.1
Basic Notions
. 1
1.2
Evolution Conservation Law
. 3
1.3
Stationary Conservation Law
. 4
1.4
Conservation Law in One Dimension
. 4
1.5
Constitutive Laws
. 6
1.6
Exercises
. 8
2
Classification, Types of Equations, Boundary and Initial Conditions
. 9
2.1
Basic Types of Equations, Boundary and Initial Conditions
. 9
2.2
Classification of Linear Equations of the Second Order
. 14
2.3
Exercises
. 17
3
Linear Partial Differential Equations of the First Order
. 21
3.1
Convection and Transport Equation
. 21
3.2
Equations with Constant Coefficients
. 22
3.3
Equations with Non-Constant Coefficients
. 28
3.4
Exercises
. 32
4
Wave Equation in One Spatial Variable
—
Cauchy Problem in
R
. 37
4.1
String Vibrations and Wave Equation in One Dimension
. 37
4.2
Cauchy Problem on the Real Line
. 40
4.3
Wave Equation with Sources
. 49
4.4
Exercises
. 53
5
Diffusion Equation in One Spatial Variable
—
Cauchy Problem in
IR
. 57
5.1
Diffusion and Heat Equations in One Dimension
. 57
5.2
Cauchy Problem on the Real Line
. 58
5.3
Diffusion Equation with Sources
. 65
5.4
Exercises
. 68
6
Laplace and
Poisson
Equations in Two Dimensions
. 71
6.1
Steady States and Laplace and
Poisson
Equations
. 71
6.2
Invariance
of the Laplace Operator, Its Transformation into Polar Co¬
ordinates
. 73
6.3
Solution of Laplace and
Poisson
Equations in R2
. 74
6.4
Exercises
. 76
vin
·
Contents
7
Solutions of Initial
Boundary Value Problems for Evolution Equations
. 78
7.1
Initial Boundary Value Problems on Half-Line
.78
7.2
Initial Boundary Value Problem on Finite Interval, Fourier Method
. 84
7.3
Fourier Method for Nonhomogeneous Problems
.99
7.4
Transformation to Simpler Problems
.103
7.5
Exercises
.104
8
Solutions of Boundary Value Problems for Stationary Equations
.113
8.1
Laplace Equation on Rectangle
.113
8.2
Laplace Equation on Disc
.115
8.3
Poisson
Formula
.117
8.4
Exercises
.119
9
Methods of Integral Transforms
.123
9.1
Laplace Transform
.123
9.2
Fourier Transform
.128
9.3
Exercises
.134
10
General Principles
.139
10.1
Principle of Causality (Wave Equation)
. 139
10.2
Energy Conservation Law (Wave Equation)
. 141
10.3
Ill-Posed Problem (Diffusion Equation for Negative t)
. 144
10.4
Maximum Principle (Heat Equation)
. 145
10.5
Energy Method (Diffusion Equation)
. 147
10.6
Maximum Principle (Laplace Equation)
. 148
10.7
Consequences of
Poisson
Formula (Laplace Equation)
. 150
10.8
Comparison of Wave, Diffusion and Laplace Equations
. 152
10.9
Exercises
. 152
11
Laplace and
Poisson
equations in Higher Dimensions
.157
11.1
Invariance
of the Laplace Operator
.157
11.2
Green's First Identity
.159
11.3
Properties of Harmonic Functions
.161
11.4
Green's Second Identity and Representation Formula
.164
11.5
Boundary Value Problems and Green's Function
.166
11.6
Dirichlet Problem on Half-Space and on Ball
.168
11.7
Exercises
.174
12
Diffusion Equation in Higher Dimensions
.178
12.1
Heat Equation in Three Dimensions
.178
12.2
Cauchy Problem in E3
.179
12.3
Diffusion on Bounded Domains, Fourier Method
.182
12.4
Exercises
.192
Contents_ jx
13
Wave Equation
in Higher
Dimensions
.I95
13.1 Membrane
Vibrations and Wave Equation
in
Two Dimensions
.
I95
13.2
Cauchy Problem in R3—
Kirchhoff
's
Formula
.196
13.3
Cauchy problem in
R2
.
I99
13.4
Wave with sources in
R3
.202
13.5
Characteristics, Singularities, Energy and Principle of Causality
. . . .204
13.6
Wave on Bounded Domains, Fourier Method
.208
13.7
Exercises
.224
14
Appendix
.228
14.1
Sturm-Liouville problem
.228
14.2
Bessel Functions
.229
Some Typical Problems Considered in This Book
.235
Notation
.237
Bibliography
.239
Index
.241 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T17:29:43Z |
| indexdate | 2024-12-04T15:01:31Z |
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| isbn | 9783110191240 3110191245 |
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| physical | IX, 245 S. graph. Darst. |
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| publisher | de Gruyter |
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| spelling | Drábek, Pavel 1953- Verfasser (DE-588)172566258 aut Elements of partial differential equations Pavel Drábek ; Gabriela Holubová Berlin [u.a.] de Gruyter 2007 IX, 245 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier de Gruyter textbook Differential equations, Partial Textbooks Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Holubová, Gabriela Verfasser (DE-588)13298654X aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2866176&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015640276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Drábek, Pavel 1953- Holubová, Gabriela Elements of partial differential equations Differential equations, Partial Textbooks Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4123623-3 |
| title | Elements of partial differential equations |
| title_auth | Elements of partial differential equations |
| title_exact_search | Elements of partial differential equations |
| title_exact_search_txtP | Elements of partial differential equations |
| title_full | Elements of partial differential equations Pavel Drábek ; Gabriela Holubová |
| title_fullStr | Elements of partial differential equations Pavel Drábek ; Gabriela Holubová |
| title_full_unstemmed | Elements of partial differential equations Pavel Drábek ; Gabriela Holubová |
| title_short | Elements of partial differential equations |
| title_sort | elements of partial differential equations |
| topic | Differential equations, Partial Textbooks Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differential equations, Partial Textbooks Partielle Differentialgleichung Lehrbuch |
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