Hyperbolic conservation laws in continuum physics

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Hyperbolic conservation laws in continuum physics / Constantine M. Dafermos

版:: 3rd ed
資料種別:: 図書
出版情報:: Heidelberg : Springer, c2010
形態:: xxxv, 708 p. ; 25 cm
シリーズ名:: Die Grundlehren der mathematischen Wissenschaften ; v. 325 <BA00007422>
著者名:: Dafermos, C. M. (Constantine M.) <DA00686025>
ISBN:: 9783642040474 [3642040470]
書誌ID:: BB01556784

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他の版・巻

Hyperbolic conservation laws in continuum physics. 4th ed
Constantine M. Dafermos , Springer , c2016

Hyperbolic conservation laws in continuum physics
Constantine M. Dafermos , Springer , c2000

書誌詳細

注記:

Includes bibliographical references (p. [597]-691) and indexes

主題:

Conservation laws (Physics); Differential equations, Hyperbolic; Field theory (Physics)

言語:

英語

目次情報:

Balance Laws / I：

Formulation of the Balance Law / 1.1：

Reduction to Field Equations / 1.2：

Change of Coordinates and a Trace Theorem / 1.3：

Systems of Balance Laws / 1.4：

Companion Balance Laws / 1.5：

Weak and Shock Fronts / 1.6：

Survey of the Theory of BV Functions / 1.7：

BV Solutions of Systems of Balance Laws / 1.8：

Rapid Oscillations and the Stabilizing Effect of Companion Balance Laws / 1.9：

Notes / 1.10：

Introduction to Continuum Physics / II：

Bodies and Motions / 2.1：

Balance Laws in Continuum Physics / 2.2：

The Balance Laws of Continuum Thermomechanics / 2.3：

Material Frame Indifference / 2.4：

Thermoelasticity / 2.5：

Thermoviscoelasticity / 2.6：

Incompressibility / 2.7：

Relaxation / 2.8：

Hyperbolic Systems of Balance Laws / 2.9：

Hyperbolicity / 3.1：

Entropy-Entropy Flux Pairs / 3.2：

Examples of Hyperbolic Systems of Balance Laws / 3.3：

The Cauchy Problem / 3.4：

The Cauchy Problem: Classical Solutions / 4.1：

Breakdown of Classical Solutions / 4.2：

The Cauchy Problem: Weak Solutions / 4.3：

Nonuniqueness of Weak Solutions / 4.4：

Entropy Admissibility Condition / 4.5：

The Vanishing Viscosity Approach / 4.6：

Initial-Boundary Value Problems / 4.7：

Entropy and the Stability of Classical Solutions / 4.8：

Convex Entropy and the Existence of Classical Solutions / 5.1：

The Role of Damping and Relaxation / 5.2：

Convex Entropy and the Stability of Classical Solutions / 5.3：

Involutions / 5.4：

Contingent Entropies and Polyconvexity / 5.5：

The L¹ Theory for Scalar Conservation Laws / 5.6：

The Cauchy Problem: Perseverance and Demise of Classical Solutions / 6.1：

Admissible Weak Solutions and their Stability Properties / 6.2：

The Method of Vanishing Viscosity / 6.3：

Solutions as Trajectories of a Contraction Semigroup / 6.4：

The Layering Method / 6.5：

A Kinetic Formulation / 6.6：

Fine Structure of L^∞ Solutions / 6.8：

The L¹Theory for Systems of Conservation Laws / 6.9：

Hyperbolic Systems of Balance Laws in One-Space Dimension / 6.11：

Balance Laws in One-Space Dimension / 7.1：

Hyperbolicity and Strict Hyperbolicity / 7.2：

Riemann Invariants / 7.3：

Genuine Nonlinearity and Linear Degeneracy / 7.4：

Simple Waves / 7.6：

Explosion of Weak Fronts / 7.7：

Existence and Breakdown of Classical Solutions / 7.8：

Weak Solutions / 7.9：

Admissible Shocks / 7.10：

Strong Shocks, Weak Shocks, and Shocks of Moderate Strength / 8.1：

The Hugoniot Locus / 8.2：

The Lax Shock Admissibility Criterion; Compressive, Overcompressive and Undercompressive Shocks / 8.3：

The Liu Shock Admissibility Criterion / 8.4：

The Entropy Shock Admissibility Criterion / 8.5：

Viscous Shock Profiles / 8.6：

Nonconservative Shocks / 8.7：

Admissible Wave Fans and the Riemann Problem / 8.8：

Self-Similar Solutions and the Riemann Problem / 9.1：

Wave Fan Admissibility Criteria / 9.2：

Solution of the Riemann Problem via Wave Curves / 9.3：

Systems with Genuinely Nonlinear or Linearly Degenerate Characteristic Families / 9.4：

General Strictly Hyperbolic Systems / 9.5：

Failure of Existence or Uniqueness; Delta Shocks and Transitional Waves / 9.6：

The Entropy Rate Admissibility Criterion / 9.7：

Viscous Wave Fans / 9.8：

Interaction of Wave Fans / 9.9：

Breakdown of Weak Solutions / 9.10：

Generalized Characteristics / 9.11：

BV Solutions / 10.1：

Extremal Backward Characteristics / 10.2：

Genuinely Nonlinear Scalar Conservation Laws / 10.4：

Admissible BV Solutions and Generalized Characteristics / 11.1：

The Spreading of Rarefaction Wives / 11.2：

Regularity of Solutions / 11.3：

Divided, Invariants and the Lax Formula / 11.4：

Decay of Solutions Induced by Entropy Dissipation / 11.5：

Spreading of Characteristics and Development of N-Waves / 11.6：

Confinement of Characteristics and Formation of Saw-toothed Profiles / 11.7：

Comparison Theorems and L¹ Stability / 11.8：

Genuinely Nonlinear Scalar Balance Laws / 11.9：

Balance Laws with Linear Excitation / 11.10：

An Inhomogeneous Conservation Law / 11.11：

Genuinely Nonlinear Systems of Two Conservation Laws / 11.12：

Notation and Assumptions / 12.1：

Entropy-Entropy Flux Pairs and the Hodograph Transformation / 12.2：

Local Structure of Solutions / 12.3：

Propagation of Riemann Invariants Along Extremal Backward Characteristics / 12.4：

Bounds on Solutions / 12.5：

Spreading of Rarefaction Waves / 12.6：

Initial Data in L¹ / 12.7：

Initial Data with Compact Support / 12.9：

Periodic Solutions / 12.10：

The Random Choice Method / 12.11：

The Construction Scheme / 13.1：

Compactness and Consistency / 13.2：

Wave Interactions, Approximate Conservation Laws and Approximate Characteristics in Genuinely Nonlinear Systems / 13.3：

The Glimm Functional for Genuinely Nonlinear Systems / 13.4：

Bounds on the Total Variation for Genuinely Nonlinear Systems / 13.5：

Bounds on the Supremum for Genuinely Nonlinear Systems / 13.6：

General Systems / 13.7：

Wave Tracing / 13.8：

Inhomogeneous Systems of Balance Laws / 13.9：

The Front Tracking Method and Standard Riemann Semigroups / 13.10：

Front Tracking for Scalar Conservation Laws / 14.1：

Front Tracking for Genuinely Nonlinear Systems of Conservation Laws / 14.2：

The Global Wave Pattern / 14.3：

Approximate Solutions / 14.4：

Bounds on the Total Variation / 14.5：

Bounds on the Combined Strength of Pseudoshocks / 14.6：

Continuous Dependence on Initial Data / 14.7：

The Standard Riemann Semigroup / 14.9：

Uniqueness of Solutions / 14.10：

Continuous Glimm Functionals, Spreading of Rarefaction Waves, and Structure of Solutions / 14.11：

Stability of Strong Waves / 14.12：

Construction of BV Solutions by the Vanishing Viscosity Method / 14.13：

The Main Result / 15.1：

Road Map to the Proof of Theorem 15.1.1 / 15.2：

The Effects of Diffusion / 15.3：

Decomposition into Viscous Traveling Waves / 15.4：

Transversal Wave Interactions / 15.5：

Interaction of Waves of the Same Family / 15.6：

Energy Estimates / 15.7：

Stability Estimates / 15.8：

Compensated Compactness / 15.9：

The Young Measure / 16.1：

Compensated Compactness and the div-curl Lemma / 16.2：

Measure-Valued Solutions for Systems of Conservation Laws and Compensated Compactness / 16.3：

Scalar Conservation Laws / 16.4：

A Relaxation Scheme for Scalar Conservation Laws / 16.5：

The System of Isentropic Elasticity / 16.6：

The System of Isentropic Gas Dynamics / 16.8：

Conservation Laws in Two Space Dimensions / 16.9：

Self-Similar Solutions for Multidimensional Scalar Conservation Laws / 17.1：

Steady Planar Isentropic Gas Flow / 17.2：

Self-Similar Planar Irrotational Isentropic Gas Flow / 17.3：

Supersonic Isentropic Gas Flow Past a Ramp of Gentle Slope / 17.4：

Regular Shock Reflection on a Wall / 17.5：

Shock Collision with a Steep Ramp / 17.6：

Bibliography / 17.7：

Author Index

Subject Index

Balance Laws / I：

Formulation of the Balance Law / 1.1：

Reduction to Field Equations / 1.2：

Change of Coordinates and a Trace Theorem / 1.3：

Systems of Balance Laws / 1.4：

Companion Balance Laws / 1.5：

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