References
G. Bartolomäus and J. Wilhelm, Existence and uniqueness of the solution of the nonstationary Boltzmann equation for the electrons in a collision dominated plasma by means of operator semigroup,Ann. Phys.,38 (1981), 211–220.
R. Beals and V. Protopopescu, Abstract time-dependent transport equations,J. Math. Anal. Appl.,121 (1987), 370–405.
H. B. Drange, On the Boltzmann equation with external forces,SIAM J. Appl. Math.,34 (1978), 577–592.
C. P. Grünfeld, On the nonlinear Boltzmann equation with force term,Transp. Theory Stat. Phys.,14 (1985), 291–322.
C. P. Grünfeld, Global solution to a mixed problem for the Boltzmann equation with Lorentz force term,Transp. Theory Stat. Phys.,15 (1986), 529–549.
H. G. Kaper, C. G. Lekkerkerker, and J. Hejtmanek,Spectral Methods in Linear Transport Theory, Birkhäuser Verlag (Basel, 1982).
F. A. Molinet, Existence, uniqueness and properties of the solutions of the Boltzmann kinetic equation for a weakly ionized gas,I. J. Math. Phys.,18 (1977), 984–996.
M. Reed and B. Simon,Methods of Mathematical Physics, Vol. 1,Functional Analysis, Academic Press (New York, 1980).
M. Tabata, Decay of solutions to the Cauchy problem for the linearized Boltzmann equation with an unbounded external-force potential,Transp. Theory Stat. Phys.,23 (1994), 741–780.
M. Tabata, Decay of solutions to the mixed problem with the periodicity boundary condition for the linearized Boltzmann equation with conservative external force,Comm. in Partial Differential Equations,18 (1993), 1823–1846.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tabata, M., Eshima, N. The spectrum of the linear transport operator with a force in a torus. Acta Math Hung 74, 63–81 (1997). https://doi.org/10.1007/BF02697877
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02697877