Abstract
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.
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References
L. Boltzmann, Sitzungsberichte der Akademie der Wissenschaften, Wien 66, 275 (1872).
C. Cercignani, “Mathematical Methods in Kinetic Theory”, Plenum Press, New York and McMillan, London (1969).
C. Cercignani, “Theory and Application of the Boltzmann Equation”, Scottish Academic Press, Edinburgh, and Elsevier, New York (1975).
S. Chapman and T. Cowling, “The Mathematical Theory of Nonuniform Gases”, Cam bridge University Press, Cambridge (1952).
S. Chandrasekhar, “Radiative Transfer”, Oxford University Press, Oxford (1950).
B. Davison, “Neutron Transport Theory”, Oxford University Press, Oxford (1957).
H.A. Kramers, Nuovo Cimento Suppl., 6, 297 (1949).
H. Grad, Phys. Fluids, 6, 147 (1963).
H. Grad, in “Rarefied Gas Dynamics”, J.A. Laurman, Ed., Vol. I, 26, Academic Press, New York (1963).
C. Cercignani, Phys. Fluids, 10, 2097 (1967).
C. Cercignani, in “Rarefied Gas Dynamics”, M. Becker and M. Fiebig, eds., Vol. I A.9, DFVLR-Press, Porz-Wahn (1974).
C. Bardos, R.E. Caflish and B. Nicolaenko, to appear (1985).
C. Cercignani, Phys. Fluids, 11, 303 (1968).
R. Beals, J. Funct. Anal. 34, 1 (1979).
W. Greenberg and C.V.M. Van der Mee, Transp. Theor. Stat. Phys. 11, 155 (1982)
C. Cercignani, J. Math. Phys., 8, 1653 (1967).
Y.P. Pao, J. Math. Phys., 8, 1893 (1967).
B.L. Willis, P.F. Zweifel and C.V.M. Van der Mee, to appear in Transp. Theor. Stat. Phys. (1985).
C. Cercignani, in “Mathematical Problems in the Kinetic Theory of Gases”, D.C. Pack and H. Neunzert, 129, P. Lang, Frankfurt (1980).
M.D. Arthur and C. Cercignani, Z. Angew. Math. Phys., 31, 634 (1980).
C.E. Siewert and J.R. Thomas, Z. Angew. Math. Phys., 32, 421 (1981).
C.E. Siewert and J.R. Thomas, Z. Angew. Math. Phys., 33, 202 (1982).
W. Greenberg and C.V.M. Van der Mee, Z. Angew. Math. Phys., 35, 156 (1984).
C. Cercignani, Ann. Phys. (NY),20, 219 (1962).
C. Cercignani, Ann. Phys. (NY), 40, 469 (1966).
C. Cercignani, Transp. Theor. Stat. Phys., 6, 29 (1977).
C. Cercignani and F. Sernagiotto, Ann, Phys. (NY), 30, 154 (1964).
C. Cercignani, Ann. Phys. (NY), 40, 454 (1966).
I.N. Vekua, “Generalized Analytic Functions”, Pergamon Press, Oxford (1962).
N.I. Muskhelishvili, “Singular Integral equations”, Noordhoff, Gromingen (1953).
C. Cercignani, Nuclear Sci. Eng., 64, 882 (1977).
B. Riemann, “Collected Works”, H. Weber, Ed., p.88, Dover Publications, New York (1953).
G. Springer, “Introduction to Riemann Surfaces”, Addison-Wesley, Reading (1957).
C.E. Siewert and C.T. Kelley, Z. Angew. Math. Phys., 31, 344 (1980).
C.E. Siewert, C.T. Kelley and R.D.M. Garcia, J. Math. Anal. Appl., 84, 509 (1981).
C.E. Siewert and J.R. Thomas, Jr., Z. Angew. Math. Phys., 33, 473 (1982).
C. Cercignani and C.E. Siewert, Z. Angew. Math. Phys., 33, 297 (1982).
K. Aoki and C. Cercignani, Z. Angew. Math. Phys., 35, 127 (1984).
K. Aoki and C. Cercignani, Z. Angew. Math. Phys., 35, 345 (1984).
K. Aoki and C. Cercignani, Z. Angew. Math. Phys., 36, 61 (1985).
R.E. Caflish, to appear in Comm. Pure Appl. Math. (1985).
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© 1986 Springer-Verlag
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Cercignani, C. (1986). Half-space problems in the kinetic theory of gases. In: Kröner, E., Kirchgässner, K. (eds) Trends in Applications of Pure Mathematics to Mechanics. Lecture Notes in Physics, vol 249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016381
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DOI: https://doi.org/10.1007/BFb0016381
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