Lü Xianqing, Mei Shengwei, Li Minshan. Exact Solutions in 1+1 Dimensions of the General Two-Velocity Discrete Illner Model[J]. Applied Mathematics and Mechanics, 1998, 19(12): 1101-1106.
 Citation: Lü Xianqing, Mei Shengwei, Li Minshan. Exact Solutions in 1+1 Dimensions of the General Two-Velocity Discrete Illner Model[J]. Applied Mathematics and Mechanics, 1998, 19(12): 1101-1106.

# Exact Solutions in 1+1 Dimensions of the General Two-Velocity Discrete Illner Model

• Rev Recd Date: 1998-05-25
• Publish Date: 1998-12-15
• The Illner,model is the most general two-velocity model of the discrete Boltoman equation.It includes,as particular cases,both the Carleman and the MeKean model.Exact solutions in 1+1 dunensions of the general two-velocity discrete Illner model can be studied in a concise way.The conclusions of the precursors need anredliorating.A new type of exact solutions in 1+1 dimensions is obtained.This gives a general method for studying non-trivial exact solutions for the similar discrete Boltzmann equation.
•  [1] M.H.Ernst,Nonlinear model-Boltzmann equation and exact solutions,Phys.Rep.,78,1(1981),1-171. [2] T.Platkowski and R.Illner,Discrete velocity models of the Boltzmann equation: a survey on the muthematical aspects of the theory,SLAM Review,30,2(1988),213-255. [3] Roberto Monaco and Luigi Preziosi,Fluid Dynamic Applications of the Discrete Boltzmann Equation,World Scientific,Singapore(1991),b3-198. [4] Henri Cornille,Exact solutions in 1+1 dimensions of the general two-velocity discrete Illner model,J.Math.Phys.,28,7(1987),1567-1579. [5] J.Wick,Two classes of explicit solutions of the Carleman model,Math.Methods Appl.Sci.,6(1984),515-519.

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