From hyperbolic systems to kinetic theory : a personalized quest

著者

• Tartar, Luc

書誌事項

From hyperbolic systems to kinetic theory : a personalized quest

Luc Tartar

（Lecture notes of the Unione matematica italiana, 6）

Springer, c2008

注記

Includes bibliographical references and index

内容説明・目次

内容説明

This fascinating book, penned by Luc Tartar of America's Carnegie Mellon University, starts from the premise that equations of state are not always effective in continuum mechanics. Tartar relies on H-measures, a tool created for homogenization, to explain some of the weaknesses in the theory. These include looking at the subject from the point of view of quantum mechanics. Here, there are no "particles", so the Boltzmann equation and the second principle, can't apply.

目次

• 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.

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詳細情報

• NII書誌ID(NCID): BA85223346
• ISBN:
  • 9783540775614
• LCCN: 2007942545
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Berlin
• ページ数/冊数: xxvii, 279 p.
• 大きさ: 24 cm
• 親書誌ID:
  • BA78039391