Open Problems and New Directions

The first eleven chapters of this book comprise a collection of much of what we (the authors) know about the Boltzmann equation for hard spheres. In this last chapter, we want to revisit some of the questions addressed in the earlier chapters and discuss some possible further developments.

[1]  J. Glimm Solutions in the large for nonlinear hyperbolic systems of equations , 1965 .

[2]  C. Cercignani,et al.  A global existence theorem for the initial-boundary-value problem for the Boltzmann equation when the boundaries are not isothermal , 1993 .

[3]  Large-time behavior of discrete velocity boltzmann equations , 1986 .

[4]  J. Bony Solutions globales bornées pour les modèles discrets de l'équation de Boltzmann en dimension $1$ d'espace , 1987 .

[5]  O. Lanford Time evolution of large classical systems , 1975 .

[6]  Existence globale et diffusion en théorie cinétique discrète , 1991 .

[7]  R. Illner,et al.  Measure solutions of the steady Boltzmann equation in a slab , 1991 .

[8]  C. Cercignani A remarkable estimate for the solutions of the Boltzmann equation , 1992 .

[9]  Pierre Degond,et al.  THE FOKKER-PLANCK ASYMPTOTICS OF THE BOLTZMANN COLLISION OPERATOR IN THE COULOMB CASE , 1992 .

[10]  A. A. Arsen’ev,et al.  ON THE CONNECTION BETWEEN A SOLUTION OF THE BOLTZMANN EQUATION AND A SOLUTION OF THE LANDAU-FOKKER-PLANCK EQUATION , 1991 .

[11]  N. Maslova Kramers problem in the kinetic theory of gases , 1982 .

[12]  Eric A. Carlen,et al.  Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation , 1992 .

[13]  A random discrete velocity model and approximation of the Boltzmann equation , 1993 .

[14]  Carlo Cercignani,et al.  Half-space problems in the kinetic theory of gases , 1986 .

[15]  Convergence of the total-approximation method for the Boltzmann equation , 1989 .