Nonlinear Boundary Value Problems in Science and Engineering
Published on 14. May 2014
433 pages
978-0-08-095870-5 (ISBN)
Description
Overall, our object has been to provide an applications-oriented text that is reasonably self-contained. It has been used as the basis for a graduate-level course both at the University of Waterloo and at the Centro Studie Applicazioni in Tecnologie Avante, Bari, Italy. The text is aimed, in the main, at applied mathematicians with a strong interest in physical applications or at engineers working in theoretical mechanics.
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Series
Language
English
Place of publication
Oxford
United States
ISBN-13
978-0-08-095870-5 (9780080958705)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Colin Rogers | William F. Ames
Nonlinear Boundary Value Problems in Science and Engineering
Book
01/1989
Academic Press
€105.23
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Content
- Front Cover
- Nonlinear Boundary Value Problems in Science and Engineering
- Copyright Page
- Contents
- Preface
- Acknowledgements
- Chapter 1. Bäcklund and Involutory Transformations
- 1.1 Bäcklund Transformations
- 1.2 Nonlinear Boundary Value Problems for the Burgers' Hierarchy. Reduction via a Bäcklund Transformation
- 1.3 Application to Nonlinear Infiltration with Prescribed Boundary Flux
- 1.4 Initial Value Problems and the Thomas Transformation. Reduction to Riemann-Volterra Canonical Form
- 1.5 Reciprocal Transformations and Nonlinear Boundary Value Problems
- 1.6 Application to Nonlinear Heat Conduction
- 1.7 Reduction of Nonlinear Boundary Value Problems via Coupled Reciprocal and Bäcklund Transformations
- 1.8 Application to Two-Phase Flow in a Porous Reservoir
- 1.9 A Generalized Reciprocal Transformation. Application in Nonlinear Visco-Elastic Wave Propagation
- 1.10 Coupled Inverse and Reciprocal Bäcklund Transformations. Reduction of a Nonlinear Shallow Water Wave System
- 1.11 A Model of Atmospheric Frontogenesis. Reduction via a Reciprocal Transformation
- Chapter 2. Bergman-Type Expansion Methods. Nonlinear Moving Boundary and Stefan-Boltzmann Problems
- 2.1 Introduction
- 2.2 1 + 1 Dimensional Stefan Problems
- 2.3 Iterated Error Integral Expansions of Bergman-Type
- 2.4 Conditions at the Moving Boundary
- 2.5 The Classical Neumann Solution
- 2.6 Single Phase Moving Boundary Problems in Nonlinear Heat Conduction
- 2.7 Two-Phase Stefan Problems in Nonlinear Heat Conduction. Application of a Reciprocal Transformation
- 2.8 A Spherical Reaction Problem
- 2.9 Heat Conduction in an Inhomogeneous Half-Space Subject to a Nonlinear Boundary Condition
- 2.10 A Stefan-Boltzmann Nonlinear Boundary Value Problem. Padé Extension of Bergman Series
- Chapter 3. Model Constitutive Laws
- 3.1 Model Constitutive Laws and Reduction to Canonical Form
- 3.2 Ermakov Systems, Nonlinear Superposition and Weak Bäcklund Transformations
- 3.3 Application to Large Amplitude Oscillation in a Thin-Walled Tube of Mooney-Rivlin Material
- 3.4 Loewner-Type Bäcklund Transformations and Nonlinear Wave Propagation. Reduction to Hyperbolic Canonical Form
- 3.5 Termination of Bergman Series and Solution of a Class of Nonlinear Cauchy Initial Value Problems
- 3.6 The Finite Plane Strain Deformation of Elastic Materials. A Class of Parametric Strain Energy Potentials. Harmonic Media
- 3.7 Adkins' Duality Principle. Application to the Plane Strain Deformation of a Mooney-Rivlin Material
- Chapter 4. Invariance Group Analysis and Its Applications
- 4.1 Introduction and Literature
- 4.2 Construction of Lie Invariance Groups. Infinitesimal Transformations. Nth Extension. Canonical Variables and Symmetry Reduction
- 4.3 Invariance Group Properties of a Nonlinear Wave Equation
- 4.4 Invariance Group Properties of a Nonlinear Visco-Elastic System
- 4.5 Lie Algebras. Commutator Tables
- 4.6 Invariant Boundaries. Application to a Class of Stefan-Type Moving Boundary Problems
- 4.7 Convective Heat Transfer in Power Law Fluids. Direct Group Analysis of a Boundary Layer System
- 4.8 Shock Propagation in Reaction Gasdynamics. Group Determination of Model Reaction Rate Laws
- 4.9 Group Invariant Deformation of a Neo-Hookean Material
- 4.10 The Von Kármán Elastic Plate Equations
- 4.11 The Soliton Connection. The Korteweg-De Vries and Kadomtsev-Petviashvili Equations
- 4.12 The Motion of a Rotating Shallow Liquid in a Rigid Container
- 4.13 Group Analysis of the Navier-Stokes Equations. Application to a Rotating Cylinder Problem
- 4.14 Lie Group Analysis of Ordinary Differential Equations
- 4.15 Conversion of Boundary Value Problems to Initial Value Problems
- 4.16 Exact Shooting and Eigenvalue Problems
- 4.17 Group Invariance and Calculation Near a Singularity
- 4.18 Group Properties and Finite Difference Schemes
- 4.19 Symmetry Group Calculations and Computer Algebra Packages
- Appendix I. Tables of Symmetry Group Generators
- A.I The 1 + 1-Dimensional Nonlinear Diffusion Equation
- A.II The Potential Burgers' Equation
- A.III The Hopf Equation
- A.IV 1-Dimensional Motion of a Visco-Plastic Material
- A.V The 2 + 1-Dimensional Classical Wave Equation
- A.VI The 1 + 1-Dimensional Semi-Linear Wave Equation
- A.VII The Nonlinear Cubic Schrödinger Equation
- A.VIII Boussinesq-Type Equations
- A.IX A Generalized Korteweg-DeVries-Burgers' Equation
- A.X A Generalized Cylindrical Kadomtsev-Petviashvili Equation
- A.XI The Jimbo-Miwa Equation
- A.XII The N-Dimensional Classical Laplace Equation
- A.XIII Liouville-Type Equations of Quantum Gravity Theory
- A.XIV Helmholtz-Type Equations in Cylindrical Co-ordinates
- A.XV The Axially-Symmetric Classical Wave Equation
- A.XVI A Three-Dimensional Nonlinear Schrödinger Equation
- A.XVII The Davey-Stewartson WaterWave System
- A.XVIII The Equations of Motion of a Polytropic Gas
- A.XIX The Non-Steady Potential Homentropic Flow Equation
- A.XX A Three-Dimensional Incompressible Boundary Layer System
- A.XXI A Three-Dimensional Steady Boundary Layer System: Arbitrary Surface
- A.XXII A Two-Dimensional Incompressible Boundary Layer System
- A.XXIII A Two-Dimensional Boundary Layer System with Prescribed Pressure
- A.XXIV A Two-Dimensional Steady Boundary Layer System with Moment Stresses
- A.XXV The 3 + 1-Dimensional Lin-Tsien Equation of Transonic Gasdynamics
- A.XXVI A Two-Dimensional Non-Steady Transonic Gasdynamics Equation
- A.XXVII A Steady Transonic Gasdynamics Equation
- A.XXVIII A Baroclinic Layer System in Oceanography
- A.XXIX 1 + 1 Dimensional Liquid Motion in Long Pipes
- A.XXX The Non-Steady Axisymmetric Incompressible Viscous Flow Equations
- A.XXXI A Steady Heat Convection System
- A.XXXII A Longitudinal One-Dimensional Plasma Motion System
- A.XXXIII A One-Dimensional Two-Component Plasma Model
- A.XXXIV A Non-Steady Dissipative Magnetohydrodynamic System
- A.XXXV A Steady Non-Dissipative Magnetohydrodynamic System
- A.XXXVI A System Descriptive of a Relativistic Pencil of Charged Particles
- A.XXXVII A Non-Linear Elastic String System
- A.XXXVIII A Nonlinear Moving Threadline System
- A.XXXIX An Elastostatic System Governing the Deformation of an Incompressible Neo-Hookean Material
- A.XXXX Maxwell's Equations in a Vacuum
- A.XXXXI Supplementary Sources of Symmetry Group Analysis
- Appendix II The Nonlinear Superposition Principle for Pinney's Equation: Derivation via Lie Group Theory
- Appendix III Glossary of Lie-Algebraic Terms
- References
- Index
- Mathematics in Science and Engineering
