Introduction to Nonlinear Differential Equations

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Introduction to Nonlinear Differential Equations / John David Logan

資料種別:: 電子ブック
出版情報:: Wiley Online Library - AutoHoldings Books
John Wiley & Sons, Inc., 2008
著者名:: Logan, John David
ISBN:: 9780470225950 [0470225955]
9780470438589 [0470438584]
書誌ID:: OB00446749

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その他の標題:

INTRODUCTION TO NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS / J. DAVID LOGAN
AN INTRODUCTION TO NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

言語:

英語

目次情報:

Preface

Introduction to Partial Differential Equations / 1：

Partial Differential Equations / 1.1：

Equations and Solutions / 1.1.1：

Classification / 1.1.2：

Linear versus Nonlinear / 1.1.3：

Linear Equations / 1.1.4：

Conservation Laws / 1.2：

One Dimension / 1.2.1：

Higher Dimensions / 1.2.2：

Constitutive Relations / 1.3：

Initial and Boundary Value Problems / 1.4：

Waves / 1.5：

Traveling Waves / 1.5.1：

Plane Waves / 1.5.2：

Plane Waves and Transforms / 1.5.3：

Nonlinear Dispersion / 1.5.4：

First-Order Equations and Characteristics / 2：

Linear First-Order Equations / 2.1：

Advection Equation / 2.1.1：

Variable Coefficients / 2.1.2：

Nonlinear Equations / 2.2：

Quasilinear Equations / 2.3：

The General Solution / 2.3.1：

Propagation of Singularities / 2.4：

General First-Order Equation / 2.5：

Complete Integral / 2.5.1：

A Uniqueness Result / 2.6：

Models in Biology / 2.7：

Age Structure / 2.7.1：

Structured Predator-Prey Model / 2.7.2：

Chemotherapy / 2.7.3：

Mass Structure / 2.7.4：

Size-Dependent Predation / 2.7.5：

Weak Solutions to Hyperbolic Equations / 3：

Discontinuous Solutions / 3.1：

Jump Conditions / 3.2：

Rarefaction Waves / 3.2.1：

Shock Propagation / 3.2.2：

Shock Formation / 3.3：

Applications / 3.4：

Traffic Flow / 3.4.1：

Plug Flow Chemical Reactors / 3.4.2：

Weak Solutions: A Formal Approach / 3.5：

Asymptotic Behavior of Shocks / 3.6：

Equal-Area Principle / 3.6.1：

Shock Fitting / 3.6.2：

Asymptotic Behavior / 3.6.3：

Hyperbolic Systems / 4：

Shallow-Water Waves; Gas Dynamics / 4.1：

Shallow-Water Waves / 4.1.1：

Small-Amplitude Approximation / 4.1.2：

Gas Dynamics / 4.1.3：

Hyperbolic Systems and Characteristics / 4.2：

The Riemann Method / 4.2.1：

Jump Conditions for Systems / 4.3.1：

Breaking Dam Problem / 4.3.2：

Receding Wall Problem / 4.3.3：

Formation of a Bore / 4.3.4：

Hodographs and Wavefronts / 4.3.5：

Hodograph Transformation / 4.4.1：

Wavefront Expansions / 4.4.2：

Weakly Nonlinear Approximations / 4.5：

Derivation of Burgers' Equation / 4.5.1：

Diffusion Processes / 5：

Diffusion and Random Motion / 5.1：

Similarity Methods / 5.2：

Nonlinear Diffusion Models / 5.3：

Reaction-Diffusion; Fisher's Equation / 5.4：

Traveling Wave Solutions / 5.4.1：

Perturbation Solution / 5.4.2：

Stability of Traveling Waves / 5.4.3：

Nagumo's Equation / 5.4.4：

Advection-Diffusion; Burgers' Equation / 5.5：

Traveling Wave Solution / 5.5.1：

Initial Value Problem / 5.5.2：

Asymptotic Solution to Burgers' Equation / 5.6：

Evolution of a Point Source / 5.6.1：

Dynamical Systems / Appendix：

Reaction-Diffusion Systems / 6：

Reaction-Diffusion Models / 6.1：

Predator-Prey Model / 6.1.1：

Combustion / 6.1.2：

Chemotaxis / 6.1.3：

Model for the Spread of a Disease / 6.2：

Contaminant Transport in Groundwater / 6.2.2：

Existence of Solutions / 6.3：

Fixed-Point Iteration / 6.3.1：

Semilinear Equations / 6.3.2：

Normed Linear Spaces / 6.3.3：

General Existence Theorem / 6.3.4：

Maximum Principles and Comparison Theorems / 6.4：

Maximum Principles / 6.4.1：

Comparison Theorems / 6.4.2：

Energy Estimates and Asymptotic Behavior / 6.5：

Calculus Inequalities / 6.5.1：

Energy Estimates / 6.5.2：

Invariant Sets / 6.5.3：

Pattern Formation / 6.6：

Equilibrium Models / 7：

Elliptic Models / 7.1：

Theoretical Results / 7.2：

Maximum Principle / 7.2.1：

Existence Theorem / 7.2.2：

Eigenvalue Problems / 7.3：

Linear Eigenvalue Problems / 7.3.1：

Nonlinear Eigenvalue Problems / 7.3.2：

Stability and Bifurcation / 7.4：

Ordinary Differential Equations / 7.4.1：

References / 7.4.2：

Index

PDEs and Solutions

Linear vs. Nonlinear

Quasi-linear Equations

The general solution

Uniqueness Result

Age-Structure

Structured predator-prey model

Mass structure

Size-dependent predation

Weak Solutions To Hyperbolic Equations

Shallow Water Waves; Gas Dynamics

Shallow Water Waves

Contaminant transport in groundwater

Semi-Linear Equations

Preface

Introduction to Partial Differential Equations / 1：

Partial Differential Equations / 1.1：

Equations and Solutions / 1.1.1：

Classification / 1.1.2：

Linear versus Nonlinear / 1.1.3：

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