连续介质物理中的双曲守恒律 (精装)
2005-1
清华大学
CONSTANTINE M.DAFERMOS
443
The seeds of Continuum Physics were planted with the works of the natural philosophers of the eighteenth century, most notably Euler, by the mid-nineteenth century, the trees were fully grown and ready to yield fruit. It was in this environment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called “hyperbolic conservation laws”; and these two subject have been traveling hand-in-hand over the past one hundred and fifty years. This book aims at presenting the theory of hyperbolic conservation laws from the standpoint of its genetic relation to Continuum Physics. Even though research is still marching at a brisk pace, both fields have attained by now the degree of maturity that would warrant the writing of such an exposition.
Chapter Ⅰ Balance Laws 1.1 Formulation of the Balance Law 1.2 Reduction to Field Equations 1.3 Change of Coordinates 1.4 Systems of Balance Laws 1.5 Companion Systems of Balance Laws 1.6 Weak and Shock Fronts 1.7 Survey of the Theory of BV Functions 1.8 BV Solutions of Systems of Balance Laws 1.9 Rapid Oscillations and the Stabilizing Effect of Companion Balance Laws 1.10 NotesChapter Ⅱ Introduction to Continuum Physics 2.1 Bodies and Motions 2.2 Balance Laws in Continuum Physics 2.3 The Balance Laws of Continuum Thermomechanics 2.4 Material Frame Indifference 2.5 Thermoelasticity 2.6 Thermoviscoelasticity 2.7 NotesChapter Ⅲ Hyperbolic Systems of Balance Laws 3.1 Hyperbolicity 3.2 Entropy-Entropy Flux Pairs 3.3 Examples of Hyperbolic Systems of Balance Laws 3.4 NotesChapter Ⅳ The Initial-Value Problem: Admissibility of Solutions 4.1 The Initial- Value Problem 4.2 The Burgers Equation and Nonuniqueness of Weak Solutions 4.3 Entropies and Admissible Solution 4.4 The Vanishing Viscosity Approach 4.5 Initial-Boundary-Value Problems 4.6 Notes Chapter Ⅴ Entropy and the Stability of Classical Solutions 5.1 Convex Entropy and the Existence of Classical Solutions 5.2 Convex Entropy and the Stability of Classical Solutions 5.3 Partially Convex Entropies and Involutions 5.4 NotesChapter Ⅵ The L1 Theory of the Scalar Conservation LawChapter Ⅶ Hyperbolic Systems of Balance Laws in One\|Space DimensionChapter Ⅷ Admissible ShocksChapter Ⅸ Admissible Wave Fans and the Riemann ProblemChapter Ⅹ Generalized CharacteristicsChapter Ⅺ Genuinely Nonlinear Scalar Conservation LawsChapter Ⅻ Genuinely Nonlinear Systems of Two Conservation LawsChapter XIII The Random Choice MethodChapter XIV The Front Tracking MethodChapter XV Compensated CompactnessBibliographyAuthor IndexSubject Index
