Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics
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| Format: | eBook |
| Language: | English |
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New York
Academic Press
1980, 1980
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| Series: | Pure and applied mathematics, a series of monographs and textbooks
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| Subjects: | |
| Online Access: | |
| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
Table of Contents:
- Part A : Continuum thermomechanics. Continuum theories of fluids ; The Stokes-Kirchhoff gas, some of its peculiarities and some of its flows
- Part B : Basic structures of the kinetic theory. The molecular density, the definitions of gross fields and the equation of evolution ; Some limits of agreement between kinetic theories and classical fluid mechanics ; The differential operators of the kinetic theory ; The dynamics of molecular encounters ; The Maxwell collisions operator
- Kinetic constitutive relations
- The total collisions operator and bilinear form ; Boltzmann's monotonicity theorem
- The Maxwellian density
- Analogues of the caloric and its flux
- Part C : The Maxwell-Boltzmann equation and its elementary consequences. The Maxwell-Boltzmann equation
- Maxwell's consistency theorem and equation of transfer ; Kinetic equilibrium and gross equilibrium
- Locally Maxwellian solutions ; Boltzmann's H[italicized]-theorem
- Epilogue
- Part D : Particular molecular models and exact solutions for moments. The collisions operator for some special kinetic constitutive relations, especially Maxwellian molecules ; The pressures and the energy flux in a gas of Maxwellian molecules
- Maxwell's relaxation theorem and evaluation of viscosity and thermal conductivity ; Homo-energetic simple shearing of a gas of Maxwellian molecules ; General solution for the pressures in homo-energetic affine flows of a gas of Maxwellian molecules
- Part E : The system of equations for the moments. The general system of equations for the moments in a gas of Maxwellian molecules
- Ikenberry's theorem on the structure of collisions integrals ; Grad's formal evaluation of collisions integrals, and his method of approximating the initial-value problem
- Part F : Existence, uniqueness and qualitative behavior. Existence theory for the general initial-value problem
- Part 1 : Molecules with intermolecular forces of infinite range ; Convergence theorems and the domain of the collisions operator ; Existence theory for the general initial-value problem
- Part 2 : Place-dependent solutions for molecules with a cut-off ; Part 3 : Spatially homogeneous solutions for molecules with a cut-off
- Part G : Grossly and momentally determined solutions and interative procedures of the kinetic theory. Hilbert's formal interative procedure for calculating gas-dynamic solutions
- The assertion of gross causality
- The Hilbert mapping ; Grossly determined solutions
- The euqations of gross determinism ; The method of stretched fields for approximating grodd determiners
- Use of it to obtain the results of Enskog's procedure ; The Maxwellian iteration of Ikenberry & Truesdell ; Convergence and divergence of atemporal Maxwellian iteration in flows for which an exact solution is known
- Failure of the higher iterates to improve the asymptotic approximation
- Includes bibliographical references (pages 569-577)