On Weak Solutions to the Linear Boltzmann Equation with Inelastic Coulomb Collisions

Journal Article · Fri May 20 00:00:00 EDT 2011 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3562634· OSTI ID:21511574

Pettersson, Rolf ^[1]

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1. Department of Mathematics, Chalmers University of Technology, SE-412 96 Goeteborg (Sweden)

This paper considers the time- and space-dependent linear Boltzmann equation with general boundary conditions in the case of inelastic (granular) collisions. First, in the (angular) cut-off case, mild L{sup 1}-solutions are constructed as limits of the iterate functions and boundedness of higher velocity moments are discussed in the case of inverse power collisions forces. Then the problem of the weak solutions, as weak limit of a sequence of mild solutions, is studied for a bounded body, in the case of very soft interactions (including the Coulomb case). Furthermore, strong convergence of weak solutions to the equilibrium, when time goes to infinity, is discussed, using a generalized H-theorem, together with a translation continuity property.

• OSTI ID: 21511574
• Journal Information: AIP Conference Proceedings, Vol. 1333, Issue 1; Conference: 27. international symposium on rarefied gas dynamics, Pacific Grove, CA (United States), 10-15 Jul 2010; Other Information: DOI: 10.1063/1.3562634; (c) 2011 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOLTZMANN EQUATION
BOUNDARY CONDITIONS
COLLISIONS
CONVERGENCE
EQUILIBRIUM
H THEOREM
INTERACTIONS
MATHEMATICAL SOLUTIONS
REFLECTION
SPACE DEPENDENCE
TIME DEPENDENCE
VELOCITY
DIFFERENTIAL EQUATIONS
EQUATIONS
INTEGRO-DIFFERENTIAL EQUATIONS
KINETIC EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS