Completely solvable models of the nonlinear Boltzmann equation I. Case of three velocities

Journal Article · Fri Nov 30 23:00:00 EST 1990 · Journal of Mathematical Physics (New York); (USA)

DOI:https://doi.org/10.1063/1.528954· OSTI ID:6038316

Osland, P ^[1]; Wu, T T ^[2]

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1. Department of Physics, University of Bergen, Allegt. 55, Bergen (Norway)
2. Gordon McKay Laboratory, Harvard University, Cambridge, MA (USA)

In one space and one time dimension, a class of models of the nonlinear Boltzmann equation is presented that is exactly solvable for all initial conditions. The models have three velocity components and the following desirable properties: (a) conservation of the number of particles; (b) energy conservation; (c) nonlinearity; (d) positivity of distribution functions; and (e) unique equilibrium state (for any given density), which is approached as {ital t}{r arrow}{infinity}. These models are very rich in structure, and some of their simple properties are studied.

• DOE Contract Number: FG02-84ER40158
• OSTI ID: 6038316
• Journal Information: Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 31:12; ISSN JMAPA; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

640410 -- Fluid Physics-- General Fluid Dynamics
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOLTZMANN EQUATION
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ENERGY CONSERVATION
EQUATIONS
EQUILIBRIUM
FUNCTIONS
NONLINEAR PROBLEMS
NUCLEAR REACTIONS
NUCLEOSYNTHESIS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLES
SYNTHESIS
THERMONUCLEAR REACTIONS
VELOCITY