Half-space problems in the kinetic theory of gases

A survey of the state-of-the art on half-space problems in kinetic theory is given, with particular concern for existence, uniqueness and closed form representations of the solutions.

[1]  George S. Springer,et al.  Introduction to Riemann Surfaces , 1959 .

[2]  C. Cercignani,et al.  On the matrix Riemann-Hilbert problem relevant to Rayleigh scattering , 1985 .

[3]  C. Cercignani,et al.  THE METHOD OF ELEMENTARY SOLUTIONS FOR TIME-DEPENDENT PROBLEMS IN LINEARIZED KINETIC THEORY , 1964 .

[4]  Robert E. Street,et al.  Mathematical Methods In Kinetic Theory , 1970 .

[5]  C. Cercignani.  Closed-form solutions for some two-group problems with anisotropic scattering , 1977 .

[6]  C. Cercignani.  Analytic solution of the temperature jump problem for the BGK model , 1977 .

[7]  H. Kramers.  On the behaviour of a gas near a wall , 1949 .

[8]  C. Mee,et al.  An abstract approach to evaporation models in rarefied gas dynamics , 1984 .

[9]  C. Mee,et al.  Abstract boundary value problems from kinetic theory , 1982 .

[10]  C. Kelley,et al.  An analytical solution to a matrix Riemann-Hilbert problem , 1980 .

[11]  C. Cercignani.  Unsteady solutions of kinetic models with velocity-dependent collision frequency , 1966 .

[12]  Raphael Aronson,et al.  Theory and application of the Boltzmann equation , 1976 .

[13]  R. Beals.  An abstract treatment of some forward-backward problems of transport and scattering , 1979 .

[14]  C. Kelley,et al.  An analytical expression for the H matrix relevant to Rayleigh scattering , 1981 .

[15]  I. Vekua.  Generalized Analytic Functions , 1962 .

[16]  C. Cercignani,et al.  A technique for time-dependent boundary value problems in the kinetic theory of gases Part I. Basic analysis , 1984 .

[17]  J. Adam.  On a class of atmospheres occurring in stellar hydrodynamic theory , 1982 .

[18]  F. Smithies,et al.  Singular Integral Equations , 1955, The Mathematical Gazette.

[19]  Mikhail Naumovich Kogan,et al.  Rarefied Gas Dynamics , 1969 .

[20]  E. Richard Cohen,et al.  Neutron Transport Theory , 1959 .

[21]  Carlo Cercignani,et al.  Elementary solutions of the linearized gas-dynamics boltzmann equation and their application to the slip-flow problem , 1962 .

[22]  C. Cercignani,et al.  Non-existence of a steady rarefied supersonic flow in a half-space , 1980 .

[23]  C. Cercignani,et al.  On partial indices for a matrix Riemann-Hilbert problem , 1982 .

[24]  C. Cercignani,et al.  A technique for time-dependent boundary value problems in the kinetic theory of gases part II. Application to sound propagation , 1984 .

[25]  Harold Grad,et al.  Asymptotic Theory of the Boltzmann Equation , 1963 .

[26]  C. Cercignani.  Existence and Uniqueness in the Large for Boundary Value Problems in Kinetic Theory , 1967 .

[27]  C. Cercignani.  Stokes Paradox in Kinetic Theory , 1968 .

[28]  C. Cercignani.  On Boltzmann Equation with Cutoff Potentials , 1967 .

[29]  J. R. Thomas,et al.  Strong evaporation into a half space. II. The three-dimensional BGK model , 1982 .

[30]  Y. Pao.  Boundary-value problems for the linearized and weakly nonlinear Boltzmann equation. , 1967 .

[31]  J. R. Thomas,et al.  Strong evaporation into a half space , 1981 .