Nonlinear Boundary Value Problems in Science and Engineering

Name: Nonlinear Boundary Value Problems in Science and Engineering
Brand: Academic Press
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Roger Ames(Autor*in)

Roger Ames(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

433 Seiten

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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

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