• Corpus ID: 220363569

On stationary solutions to normal, coplanar, discrete Boltzmann equation models

  title={On stationary solutions to normal, coplanar, discrete Boltzmann equation models},
  author={L.Arkeryd and A.Nouri},
The paper proves existence of renormalized solutions for a class of velocity-discrete coplanar stationary Boltzmann equations with given indata. The proof is based on the construction of a sequence of approximations with L1 compactness for the integrated collision frequency and gain term. L1 compactness of a sequence of approximations is obtained using the Kolmogorov-Riesz theorem and replaces the L1 compactness of velocity averages in the continuous velocity case, not available when the… 



A Consistency Result for a Discrete-Velocity Model of the Boltzmann Equation

It is proved that it is possible to construct models consistent with the Boltzmann equation, i.e., such that the discrete collision term can be seen as an approximation of the collision integral of the BoltZmann equation.

Exact Solutions of Discrete Kinetic Models and Stationary Problems for the Plane Broadwell Model

A review of exact solutions of discrete velocity models is given. Different methods of constructing the solutions are discussed. New methods are proposed for the stationary Broadwell model, and new

Stationary solutions to the two-dimensional Broadwell model

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Discrete velocity models of the Boltzmann equation are of considerable conceptual interest in the kinetic theory of gases, and, at the same time, a fascinating mathematical subject. The last decade

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Sur des critères d'existence globale en théorie cinétique discrète

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A boundary value problem for the two dimensional Broadwell model

It is shown that a certain boundary value problem for the steady two-dimensional Broadwell model on a rectangle has a solution. The boundary conditions specify the ingoing particle densities on each


Ueber Kompaktheit dr Funktionenmengen bei der Konvergenz im Mittel

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We study the large-data Cauchy problem for Boltzmann equations with general collision kernels. We prove that sequences of solutions which satisfy only the physically natural a priori bounds converge