UID:
almahu_9947367172102882
Format:
1 online resource (433 p.)
ISBN:
1-282-28985-3
,
9786612289859
,
0-08-095870-2
Series Statement:
Mathematics in science and engineering ; 183
Content:
Nonlinear boundary value problems in science and engineering
Note:
Description based upon print version of record.
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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
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1.6 Application to Nonlinear Heat Conduction1.7 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
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Chapter 2. Bergman-Type Expansion Methods. Nonlinear Moving Boundary and Stefan-Boltzmann Problems2.1 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
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2.10 A Stefan-Boltzmann Nonlinear Boundary Value Problem. Padé Extension of Bergman SeriesChapter 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
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3.6 The Finite Plane Strain Deformation of Elastic Materials. A Class of Parametric Strain Energy Potentials. Harmonic Media3.7 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
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4.5 Lie Algebras. Commutator Tables
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English
Additional Edition:
ISBN 0-12-593110-7
Language:
English
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