On stationary solutions to normal, coplanar discrete Boltzmann equation models

Exact Solutions for Some Discrete Models of the Boltzmann Equation

Abs tra ct. For the simplest of the disc rete mod els of the Boltzmann equations , the Broad well model, exact solutions have been obtained by Co rnille [15.16] in the form of bisolitons. In the present paper, we build exact solutions for more co mplex mod els. 1. Introduction For t he las t twenty years, t he st udy of disc rete mo de ls of t he Bolt zm ann equat ion h as attract ed t he atten...

Superabundance of Stationary Solutions for the Discrete Allen-cahn Equation

The discrete Allen-Cahn equation is a spatially discrete analogue of the Allen-Cahn equation, a parabolic partial differential equation proposed as a simple model for phase separation in materials. In some sense, the solutions of the discrete equation display a richer variety of behaviors than do the corresponding solutions of the continuous equation. In particular, the number of stationary sol...

On the Stationary Boltzmann Equation in R N

Regularity of Stationary Solutions to the Linearized Boltzmann Equations

Abstract. We consider the regularity of the solutions to the stationary linearized Boltzmann equations in bounded C convex domains in R for gases with cutoff hard potential and cutoff Maxwellian gases. Suppose that a solution has a bounded weighted L norm in space and velocity with the weight of collision frequency, which is a typical functional space for existence results for boundary value pr...

Stationary waves for the discrete Boltzmann equation in the half space with reflective boundaries

where each F = (Fi)i∈Λ is an unknown function representing the mass density of gas particles; Λ is a finite set {1, 2, . . .m} and Λ± := {i ∈ Λ : vi ≷ 0}; each νi is a positive integer; each vi is a constant representing the x-component of the i-th velocity and vi’s are not necessarily distinct and not necessarily non-zero; each Qi(F ) is a given function called the collision term; each Bij is ...