Existence and quantitative analysis of the solutions to the initial value problem for the discrete Boltzmann equation in all space
Abstract
In this paper, a mathematical method capable of providing quantitative results for discrete velocities models in kinetic theory of gases is studied. This method requires that the solution of the kinetic equation be differentiable with respect to the space. Therefore, for such a class of solutions, local and global in time, existence proofs for the Cauchy problem in all space are provided. Finally, a suitable application with a sixvelocities plane model is proposed.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 August 1989
 Bibcode:
 1989SJAM...49.1231L
 Keywords:

 Boltzmann Transport Equation;
 Existence Theorems;
 Quantitative Analysis;
 Boundary Value Problems;
 Cauchy Problem;
 Kinetic Theory;
 Thermodynamics and Statistical Physics