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Elements of Partial Differential Equations

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ISBN-10: 3110191245

ISBN-13: 9783110191240

Edition: 2007

Authors: Pavel Drabek, Gabriela Holubov�

List price: $45.00
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Book details

List price: $45.00
Copyright year: 2007
Publisher: De Gruyter, Inc.
Publication date: 2/19/2007
Binding: Paperback
Pages: 254
Size: 6.50" wide x 9.00" long x 0.50" tall
Weight: 0.990
Language: English

Preface
Mathematical Models, Conservation and Constitutive Laws
Basic Notions
Evolution Conservation Law
Stationary Conservation Law
Conservation Law in One Dimension
Constitutive Laws
Exercises
Classification, Types of Equations, Boundary and Initial Conditions
Basic Types of Equations, Boundary and Initial Conditions
Classification of Linear Equations of the Second Order
Exercises
Linear Partial Differential Equations of the First Order
Convection and Transport Equation
Equations with Constant Coefficients
Equations with Non-Constant Coefficients
Exercises
Wave Equation in One Spatial Variable-Cauchy Problem in R
String Vibrations and Wave Equation in One Dimension
Cauchy Problem on the Real Line
Wave Equation with Sources
Exercises
Diffusion Equation in One Spatial Variable-Cauchy Problem in R
Diffusion and Heat Equations in One Dimension
Cauchy Problem on the Real Line
Diffusion Equation with Sources
Exercises
Laplace and Poisson Equations in Two Dimensions
Steady States and Laplace and Poisson Equations
Invariance of the Laplace Operator, Its Transformation into Polar Coordinates
Solution of Laplace and Poisson Equations in R[superscript 2]
Exercises
Solutions of Initial Boundary Value Problems for Evolution Equations
Initial Boundary Value Problems on Half-Line
Initial Boundary Value Problem on Finite Interval, Fourier Method
Fourier Method for Nonhomogeneous Problems
Transformation to Simpler Problems
Exercises
Solutions of Boundary Value Problems for Stationary Equations
Laplace Equation on Rectangle
Laplace Equation on Disc
Poisson Formula
Exercises
Methods of Integral Transforms
Laplace Transform
Fourier Transform
Exercises
General Principles
Principle of Causality (Wave Equation)
Energy Conservation Law (Wave Equation)
Ill-Posed Problem (Diffusion Equation for Negative t)
Maximum Principle (Heat Equation)
Energy Method (Diffusion Equation)
Maximum Principle (Laplace Equation)
Consequences of Poisson Formula (Laplace Equation)
Comparison of Wave, Diffusion and Laplace Equations
Exercises
Laplace and Poisson equations in Higher Dimensions
Invariance of the Laplace Operator
Green's First Identity
Properties of Harmonic Functions
Green's Second Identity and Representation Formula
Boundary Value Problems and Green's Function
Dirichlet Problem on Half-Space and on Ball
Exercises
Diffusion Equation in Higher Dimensions
Heat Equation in Three Dimensions
Cauchy Problem in R[superscript 3]
Diffusion on Bounded Domains, Fourier Method
Exercises
Wave Equation in Higher Dimensions
Membrane Vibrations and Wave Equation in Two Dimensions
Cauchy Problem in R[superscript 3]-Kirchhoff's Formula
Cauchy problem in R[superscript 2]
Wave with sources in R[superscript 3]
Characteristics, Singularities, Energy and Principle of Causality
Wave on Bounded Domains, Fourier Method
Exercises
Appendix
Sturm-Liouville problem
Bessel Functions
Some Typical Problems Considered in This Book
Notation
Bibliography
Index