1 (p1): I Balance Laws2 (p1-1): 1.1 Formulation of the Balance Law3 (p1-2): 1.2 Reduction to Field Equations7 (p1-3): 1.3 Change of Coordinates and a Trace Theorem12 (p1-4): 1.4 Systems of Balance Laws13 (p1-5): 1.5 Companion Balance Laws15 (p1-6): 1.6 Weak and Shock Fronts17 (p1-7): 1.7 Survey of the Theory of BV Functions21 (p1-8): 1.8 BV Solutions of Systems of Balance Laws22 (p1-9): 1.9 Rapid Oscillations and the Stabilizing Effect of Companion Balance Laws23 (p1-10): 1.10 Notes25 (p2): II Introduction to Continuum Physics25 (p2-1): 2.1 Bodies and Motions28 (p2-2): 2.2 Balance Laws in Continuum Physics31 (p2-3): 2.3 The Balance Laws of Continuum Thermomechanics35 (p2-4): 2.4 Material Frame Indifference36 (p2-5): 2.5 Thermoelasticity44 (p2-6): 2.6 Thermoviscoelasticity47 (p2-7): 2.7 Incompressibility48 (p2-8): 2.8 Relaxation49 (p2-9): 2.9 Notes53 (p3): III Hyperbolic Systems of Balance Laws53 (p3-1): 3.1 Hyperbolicity54 (p3-2): 3.2 Entropy-Entropy Flux Pairs56 (p3-3): 3.3 Examples of Hyperbolic Systems of Balance Laws72 (p3-4): 3.4 Notes75 (p4): IV The Cauchy Problem75 (p4-1): 4.1 The Cauchy Problem:Ciassical Solutions78 (p4-2): 4.2 Breakdown ofClassical Solutions81 (p4-3): 4.3 The Cauchy Problem:Weak Solutions82 (p4-4): 4.4 Nonuniqueness of Weak Solutions83 (p4-5): 4.5 Entropy Admissibility Condition87 (p4-6): 4.6 The Vanishing Viscosity Approach91 (p4-7): 4.7 Initial-Boundary Value Problems95 (p4-8): 4.8 Notes97 (p5): V Entropy and the Stability of Classical Solutions98 (p5-1): 5.1 Convex Entropy and the Existence of Classical Solutions108 (p5-2): 5.2 The Role ofDamping and Relaxation116 (p5-3): 5.3 Convex Entropy and the Stability of Classical Solutions119 (p5-4): 5.4 Involutions129 (p5-5): 5.5 Contingent Entropies and Polyconvexity138 (p5-6): 5.6 Initial-Boundary Value Problems141 (p5-7): 5.7 Notes145 (p6): VI The L1 Theory for Scalar Conservation Laws146 (p6-1): 6.1 The Cauchy Problem:Perseverance and Demise of...

zlibzh/no-category/（美）达夫莫斯著/连续介质物理中的双曲守恒律 第3版=HYPERBOLIC CONSERVATION LAWS IN CONTINUUM PHYSICS THIRD EDITION 英文_34408255.pdf

Bookmarks: p1 (p1): Ⅰ Balance Laws
p1-1 (p2): 1.1 Formulation of the Balance Law
p1-2 (p3): 1.2 Reduction to Field Equations
p1-3 (p7): 1.3 Change of Coordinates and a Trace Theorem
p1-4 (p12): 1.4 Systems of Balance Laws
p1-5 (p13): 1.5 Companion Balance Laws
p1-6 (p15): 1.6 Weak and Shock Fronts
p1-7 (p17): 1.7 Survey of the Theory of BV Functions
p1-8 (p21): 1.8 BV Solutions of Systems of Balance Laws
p1-9 (p22): 1.9 Rapid Oscillations and the Stabilizing Effect of Companion Balance Laws
p1-10 (p23): 1.10 Notes
p2 (p25): Ⅱ Introduction to Continuum Physics
p2-1 (p25): 2.1 Bodies and Motions
p2-2 (p28): 2.2 Balance Laws in Continuum Physics
p2-3 (p31): 2.3 The Balance Laws of Continuum Thermomechanics
p2-4 (p35): 2.4 Material Frame Indifference
p2-5 (p36): 2.5 Thermoelasticity
p2-6 (p44): 2.6 Thermoviscoelasticity
p2-7 (p47): 2.7 Incompressibility
p2-8 (p48): 2.8 Relaxation
p2-9 (p49): 2.9 Notes
p3 (p53): Ⅲ Hyperbolic Systems of Balance Laws
p3-1 (p53): 3.1 Hyperbolicity
p3-2 (p54): 3.2 Entropy-Entropy Flux Pairs
p3-3 (p56): 3.3 Examples of Hyperbolic Systems of Balance Laws
p3-4 (p72): 3.4 Notes
p4 (p75): Ⅳ The Cauchy Problem
p4-1 (p75): 4.1 The Cauchy Problem:Ciassical Solutions
p4-2 (p78): 4.2 Breakdown ofClassical Solutions
p4-3 (p81): 4.3 The Cauchy Problem:Weak Solutions
p4-4 (p82): 4.4 Nonuniqueness of Weak Solutions
p4-5 (p83): 4.5 Entropy Admissibility Condition
p4-6 (p87): 4.6 The Vanishing Viscosity Approach
p4-7 (p91): 4.7 Initial-Boundary Value Problems
p4-8 (p95): 4.8 Notes
p5 (p97): Ⅴ Entropy and the Stability of Classical Solutions
p5-1 (p98): 5.1 Convex Entropy and the Existence of Classical Solutions
p5-2 (p108): 5.2 The Role ofDamping and Relaxation
p5-3 (p116): 5.3 Convex Entropy and the Stability of Classical Solutions
p5-4 (p119): 5.4 Involutions
p5-5 (p129): 5.5 Contingent Entropies and Polyconvexity
p5-6 (p138): 5.6 Initial-Boundary Value Problems
p5-7 (p141): 5.7 Notes
p6 (p145): Ⅵ The L1 Theory for Scalar Conservation Laws
p6-1 (p146): 6.1 The Cauchy Problem:Perseverance and Demise of Classical Solutions
p6-2 (p148): 6.2 Admissible Weak Solutions and their Stability Properties
p6-3 (p153): 6.3 The Method of Vanishing Viscosity
p6-4 (p158): 6.4 Solutions as Trajectories of a Contraction Semigroup
p6-5 (p164): 6.5 The Layering Method
p6-6 (p167): 6.6 Relaxation
p6-7 (p174): 6.7 A Kinetic Formulation
p6-8 (p180): 6.8 Fine Structure of L∞ Solutions
p6-9 (p183): 6.9 Initial-Boundary Value Problems
p6-10 (p188): 6.10 The L1 Theory for Systems of Conservation Laws
p6-11 (p192): 6.11 Notes
p7 (p195): Ⅶ Hyperbolic Systems of Balance Laws in One-Space Dimension
p7-1 (p195): 7.1 Balance Laws in One-Space Dimension
p7-2 (p203): 7.2 Hyperbolicity and Strict Hyperbolicity
p7-3 (p206): 7.3 Riemann Invariants
p7-4 (p211): 7.4 Entropy-Entropy Flux Pairs
p7-5 (p214): 7.5 Genuine Nonlinearity and Linear Degeneracy
p7-6 (p216): 7.6 Simple Waves
p7-7 (p220): 7.7 Explosion of Weak Fronts
p7-8 (p221): 7.8 Existence and Breakdown of Classical Solutions
p7-9 (p225): 7.9 Weak Solutions
p7-10 (p226): 7.10 Notes
p8 (p231): Ⅷ Admissible Shocks
p8-1 (p231): 8.1 Strong Shocks,Weak Shocks,and Shocks of Moderate Strength
p8-2 (p234): 8.2 The Hugoniot Locus
p8-3 (p240): 8.3 The Lax Shock Admissibility Criterion;Compressive,Overcompressive and Undercompressive Shocks
p8-4 (p246): 8.4 The Liu Shock Admissibility Criterion
p8-5 (p248): 8.5 The Entropy Shock Admissibility Criterion
p8-6 (p252): 8.6 Viscous Shock Profiles
p8-7 (p264): 8.7 Nonconservative Shocks
p8-8 (p265): 8.8 Notes
p9 (p271): Ⅸ Admissible Wave Fans and the Riemann Problem
p9-1 (p271): 9.1 Self-Similar Solutions and the Riemann Problem
p9-2 (p274): 9.2 Wave Fan Admissibility Criteria
p9-3 (p275): 9.3 Solution of the Riemann Problem via Wave Curves
p9-4 (p278): 9.4 Systems with Genuinely Nonlinear or Linearly Degenerate Characteristic Families
p9-5 (p283): 9.5 General Strictly Hyperbolic Systems
p9-6 (p287): 9.6 Failure of Existence or Uniqueness;Delta Shocks and Transitional Waves
p9-7 (p290): 9.7 The Entropy Rate Admissibility Criterion
p9-8 (p299): 9.8 Viscous Wave Fans
p9-9 (p309): 9.9 Interaction of Wave Fans
p9-10 (p317): 9.10 Breakdown of Weak Solutions
p9-11 (p320): 9.11 Notes
p10 (p325): Ⅹ Generalized Characteristics
p10-1 (p325): 10.1 BV Solutions
p10-2 (p326): 10.2 Generalized Characteristics
p10-3 (p328): 10.3 Extremal Backward Characteristics
p10-4 (p330): 10.4 Notes
p11 (p331): Ⅺ Genuinely Nonlinear Scalar Conservation Laws
p11-1 (p332): 11.1 Admissible BV Solutions and Generalized Characteristics
p11-2 (p335): 11.2 The Spreading of Rarefaction Waves
p11-3 (p336): 11.3 Regularity of Solutions
p11-4 (p340): 11.4 Divides,Invariants and the Lax Formula
p11-5 (p344): 11.5 Decay of Solutions Induced by Entropy Dissipation
p11-6 (p346): 11.6 Spreading of Characteristics and Development of N-Waves
p11-7 (p348): 11.7 Confinement of Characteristics and Formation of Saw-toothed Profiles
p11-8 (p350): 11.8 Comparison Theorems and L1 Stability
p11-9 (p358): 11.9 Genuinely Nonlinear Scalar Balance Laws
p11-10 (p362): 11.10 Balance Laws with Linear Excitation
p11-11 (p365): 11.11 An Inhomogeneous Conservation Law
p11-12 (p370): 11.12 Notes
p12 (p373): Ⅻ Genuinely Nonlinear Systems of Two Conservation Laws
p12-1 (p373): 12.1 Notation and Assumptions
p12-2 (p375): 12.2 Entropy-Entropy Flux Pairs and the Hodograph Transformation
p12-3 (p378): 12.3 Local Structure of Solutions
p12-4 (p381): 12.4 Propagation of Riemann Invariants Along Extremal Backward Characteristics
p12-5 (p398): 12.5 Bounds on Solutions
p12-6 (p410): 12.6 Spreading of Rarefaction Waves
p12-7 (p415): 12.7 Regularity of Solutions
p12-8 (p417): 12.8 Initial Data in L1
p12-9 (p421): 12.9 Initial Data with Compact Support
p12-10 (p427): 12.10 Periodic Solutions
p12-11 (p432): 12.11 Notes
p13 (p435): ⅩⅢ The Random Choice Method
p13-1 (p435): 13.1 The Construction Scheme
p13-2 (p438): 13.2 Compactness and Consistency
p13-3 (p444): 13.3 Wave Interactions,Approximate Conservation Laws and Approximate Characteristics in Genuinely Nonlinear Systems
p13-4 (p448): 13.4 The Glimm Functional for Genuinely Nonlinear Systems
p13-5 (p453): 13.5 Bounds on the Total Variation for Genuinely Nonlinear Systems
p13-6 (p455): 13.6 Bounds on the Supremum for Genuinely Nonlinear Systems
p13-7 (p457): 13.7 General Systems
p13-8 (p460): 13.8 Wave Tracing
p13-9 (p463): 13.9 Inhomogeneous Systems of Balance Laws
p13-10 (p474): 13.10 Notes
p14 (p477): ⅩⅣ The Front Tracking Method and Standard Riemann Semigroups
p14-1 (p478): 14.1 Front Tracking for Scalar Conservation Laws
p14-2 (p480): 14.2 Front Tracking for Genuinely Nonlinear Systems of Conservation Laws
p14-3 (p485): 14.3 The Global Wave Pattern
p14-4 (p486): 14.4 Approximate Solutions
p14-5 (p488): 14.5 Bounds on the Total Variation
p14-6 (p491): 14.6 Bounds on the Combined Strength of Pseudoshocks
p14-7 (p494): 14.7 Compactness and Consistency
p14-8 (p496): 14.8 Continuous Dependence on Initial Data
p14-9 (p500): 14.9 The Standard Riemann Semigroup
p14-10 (p501): 14.10 Uniqueness of Solutions
p14-11 (p507): 14.11 Continuous Glimm Functionals,Spreading of Rarefaction Waves,and Structure of Solutions
p14-12 (p510): 14.12 Stability of Strong Waves
p14-13 (p512): 14.13 Notes
p15 (p517): ⅩⅤ Construction of BV Solutions by the Vanishing Viscosity Method
p15-1 (p517): 15.1 The Main Result
p15-2 (p519): 15.2 Road Map to the ProofofTheorem 15.1.1
p15-3 (p521): 15.3 The Effects of Diffusion
p15-4 (p524): 15.4 Decomposition into Viscous Traveling Waves
p15-5 (p528): 15.5 Transversal Wave Interactions
p15-6 (p532): 15.6 Interaction of Waves of the Same Family
p15-7 (p536): 15.7 Energy Estimates
p15-8 (p539): 15.8 Stability Estimates
p15-9 (p542): 15.9 Notes
p16 (p545): ⅩⅥ Compensated Compactness
p16-1 (p546): 16.1 The Young Measure
p16-2 (p547): 16.2 Compensated Compactness and the div-curl Lemma
p16-3 (p548): 16.3 Measure-Valued Solutions for Systems of Conservation Laws and Compensated Compactness
p16-4 (p551): 16.4 Scalar Conservation Laws
p16-5 (p553): 16.5 A Relaxation Scheme for Scalar Conservation Laws
p16-6 (p556): 16.6 Genuinely Nonlinear Systems of Two Conservation Laws
p16-7 (p559): 16.7 The System of Isentropic Elasticity
p16-8 (p564): 16.8 The System of Isentropic Gas Dynamics
p16-9 (p567): 16.9 Notes
p17 (p573): ⅩⅦ Conservation Laws in Two Space Dimensions
p17-1 (p573): 17.1 Self-Similar Solutions for Multidimensional Scalar Conservation Laws
p17-2 (p576): 17.2 Steady Planar Isentropic Gas Flow
p17-3 (p580): 17.3 Self-Similar Planar Irrotational Isentropic Gas Flow
p17-4 (p583): 17.4 Supersonic Isentropic Gas Flow Past a Ramp of Gentle Slope
p17-5 (p588): 17.5 Regular Shock Reflection on a Wall
p17-6 (p591): 17.6 Shock Collision with a Steep Ramp
p17-7 (p594): 17.7 Notes
p18 (p597): Bibliography
p19 (p693): Author Index
p20 (p703): Subject Index

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2024-06-13