From Hyperbolic Systems to Kinetic Theory

1.Historical Perspective.- 2.Hyperbolic Systems: Riemann Invariants, Rarefaction Waves.- 3.Hyperbolic Systems: Contact Discontinuities, Shocks.- 4.The Burgers Equation and the 1-D Scalar Case.- 5.The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik.- 6.Hopf's Formulation of the E-Condition of Oleinik.- 7.The Burgers Equation: Special Solutions.- 8.The Burgers Equation: Small Perturbations; the Heat Equation.- 9.Fourier Transform; the Asymptotic Behaviour for the Heat Equation.- 10.Radon Measures; the Law of Large Numbers.- 11.A 1-D Model with Characteristic Speed 1/epsilon.- 12.A 2-D Generalization; the Perron-Frobenius Theory.- 13.A General Finite-Dimensional Model with Characteristic Speed 1/epsilon.- 14.Discrete Velocity Models.- 15.The Mimura-Nishida and the Crandall-Tartar Existence Theorems.- 16.Systems Satisfying My Condition (S).- 17.Asymptotic Estimates for the Broadwell and the Carleman Models.- 18.Oscillating Solutions; the 2-D Broadwell Model.- 19.Oscillating Solutions: the Carleman Model.- 20.The Carleman Model: Asymptotic Behaviour.- 21.Oscillating Solutions: the Broadwell Model.- 22.Generalized Invariant Regions; the Varadhan Estimate.- 23.Questioning Physics; from Classical Particles to Balance Laws.- 24.Balance Laws; What Are Forces?- 25.D. Bernoulli: from Masslets and Springs to the 1-D Wave Equation.- 26.Cauchy: from Masslets and Springs to 2-D Linearized Elasticity.- 27.The Two-Body Problem.- 28.The Boltzmann Equation.- 29.The Illner-Shinbrot and the Hamdache Existence Theorems.- 30.The Hilbert Expansion.- 31.Compactness by Integration.- 32.Wave Front Sets; H-Measures.- 33.H-Measures and 'Idealized Particles'.- 34.Variants of H-Measures.- 35.Biographical Information.- 36.Abbreviations and Mathematical Notation.- References.- Index.

From the reviews:



"The book is well organized. ... Tartar is excellent in bringing out the essence of ideas and methods ... . The monograph is an interesting read from more than one point of view. First, the mathematically literate reader finds an extensive ... review of the relevant subjects; reading the sketches of proofs offers a bird's eye view of the underlying concepts as well as the exceptional mind of the author. ... All in all, a remarkable book." (Reinhard Illner, SIAM Reviews, Vol. 51 (2), June, 2009)

"This is a very nice book devoted to hyperbolic systems of conservation laws. ... This book can be recommended to all researchers in respective areas, especially to graduate students."­­­ (Mitsuru Yamazaki, Mathematical Reviews, Issue 2010 j)