From Hyperbolic Systems to Kinetic Theory : A Personalized Quest
Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical re...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | Livre numérique |
| اللغة: | Anglais |
| منشور في: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| سلاسل: | Lecture Notes of the Unione Matematica Italiana
6 |
| الموضوعات: | |
| الوصول للمادة أونلاين: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| ملاحظة: |
L'impression du document génère 294 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • From hyperbolic systems to kinetic theory, a personalized quest, Luc Tartar, Berlin, Springer, 2008, 1 vol. (XXVII-279 p.), Lecture notes of the Unione Matematica Italiana, 978-3-540-77561-4 |
| LEADER | 05009nam a22004697a 4500 | ||
|---|---|---|---|
| 001 | 940299 | ||
| 008 | 080505q2000 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN123743346 | ||
| 020 | |a 9783540775621 | ||
| 041 | 0 | |a eng | |
| 082 | |a 515.353 | ||
| 084 | |a 35-02. 2010 | ||
| 084 | |a 35Lxx. 2010 | ||
| 084 | |a 35Q30. 2010 | ||
| 084 | |a 70F45. 2010 | ||
| 084 | |a 76A02. 2010 | ||
| 084 | |a 76N15. 2010 | ||
| 084 | |a 76P05. 2010 | ||
| 084 | |a 82C22. 2010 | ||
| 100 | 1 | |a Tartar, Luc, |d 1946- | |
| 245 | 1 | 0 | |a From Hyperbolic Systems to Kinetic Theory : |b A Personalized Quest |c Luc Tartar. |
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Lecture Notes of the Unione Matematica Italiana |v 6 | |
| 500 | |a L'impression du document génère 294 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a Historical Perspective Hyperbolic Systems: Riemann Invariants, Rarefaction Waves Hyperbolic Systems: Contact Discontinuities, Shocks The Burgers Equation and the 1-D Scalar Case The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik Hopf's Formulation of the E-Condition of Oleinik The Burgers Equation: Special Solutions The Burgers Equation: Small Perturbations; the Heat Equation Fourier Transform; the Asymptotic Behaviour for the Heat Equation Radon Measures; the Law of Large Numbers A 1-D Model with Characteristic Speed 1/? A 2-D Generalization; the Perron Frobenius Theory A General Finite-Dimensional Model with Characteristic Speed 1/? Discrete Velocity Models The Mimura Nishida and the Crandall Tartar Existence Theorems Systems Satisfying My Condition (S) Asymptotic Estimates for the Broadwell and the Carleman Models Oscillating Solutions; the 2-D Broadwell Model Oscillating Solutions: the Carleman Model The Carleman Model: Asymptotic Behaviour Oscillating Solutions: the Broadwell Model Generalized Invariant Regions; the Varadhan Estimate Questioning Physics; from Classical Particles to Balance Laws Balance Laws; What Are Forces? D. Bernoulli: from Masslets and Springs to the 1-D Wave Equation Cauchy: from Masslets and Springs to 2-D Linearized Elasticity The Two-Body Problem The Boltzmann Equation The Illner Shinbrot and the Hamdache Existence Theorems The Hilbert Expansion Compactness by Integration Wave Front Sets; H-Measures H-Measures and Idealized Particles Variants of H-Measures Biographical Information Abbreviations and Mathematical Notation. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity! | ||
| 650 | |a Équations différentielles hyperboliques | ||
| 650 | |a Physique mathématique | ||
| 650 | |a Gaz, Théorie cinétique des | ||
| 776 | 0 | |0 127378812 |t From hyperbolic systems to kinetic theory |o a personalized quest |f Luc Tartar |c Berlin |n Springer |d 2008 |p 1 vol. (XXVII-279 p.) |s Lecture notes of the Unione Matematica Italiana |z 978-3-540-77561-4 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-3-540-77562-1 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-KJX13C1P-Z |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:747862303 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.1007/978-3-540-77562-1 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:750879823 |u https://ezproxy.insa-cvl.fr/login?qurl=https://doi.org/10.1007/978-3-540-77562-1 |z Accès INSA CVL | |
| 997 | |0 940299 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||