Positive similarity solutions for a discrete velocity Boltzmann coagulation-fragmentation model

H. Cornille (1) , M. Ikle

1 SPhT - Service de Physique Théorique

We consider the Slemrod et al$^{(1)}$ coagulation-fragmentation model which is essentially the 2-dimensional Broadwell model including inelastic collisions. We construct two classes of similarity solutions (variable $\eta =x-\zeta t$), positive for $\eta \in (-\infty ,\infty )$: the Rankine-Hugoniot solutions and the scalar Riccati similarity solutions. Previous solutions were built up with positivity along half of the x-axis. For the two classes we determine in the parameter space, building up the solutions, domains corresponding to positive solutions.

Domaines: Physique Générale [physics.gen-ph]

H. Cornille, M. Ikle. Positive similarity solutions for a discrete velocity Boltzmann coagulation-fragmentation model. Letters in Mathematical Physics, 1995, 34, pp.9-16. ⟨hal-00162814⟩