The spectrum of the transport operator with a potential term under the spatial periodicity condition
Rendiconti del Seminario Matematico della Università di Padova, Tome 97 (1997), pp. 211-233. 
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     author = {Tabata, Minoru and Eshima, Nobuoki},
     title = {The spectrum of the transport operator with a potential term under the spatial periodicity condition},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {211--233},
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     volume = {97},
     year = {1997},
     mrnumber = {1476172},
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     url = {http://archive.numdam.org/item/RSMUP_1997__97__211_0/}
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Tabata, Minoru; Eshima, Nobuoki. The spectrum of the transport operator with a potential term under the spatial periodicity condition. Rendiconti del Seminario Matematico della Università di Padova, Tome 97 (1997), pp. 211-233. http://archive.numdam.org/item/RSMUP_1997__97__211_0/

[1] R. Beals - V. PROTOPOPESCU, Abstract time-dependent transport equations, J. Math. Anal. Appl., 121 (1987), pp. 370-405. | MR | Zbl

[2] G. Bartolomäus - 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), pp. 211-220. | MR

[3] N. Bellomo - M. LACHOWICZ - A. PALCZEWSKI - G. TOSCANI, On the initial value problem for the Boltzmann equation with a force term, Transp. Theory Stat. Phys., 18 (1989), pp. 87-102. | MR | Zbl

[4] H.B. Drange, On the Boltzmann equation with external forces, SIAM J. Appl. Math., 34 (1978), pp. 577-592. | MR | Zbl

[5] H. Grad, Asymptotic theory of the Boltzmann equation, II, in Rarefied Gas Dynamics (J. A. LAURMANN Ed.), Academic Press, New York (1963), pp. 26-59. | MR

[6] C.P. Grünfeld, On the nonlinear Boltzmann equation with force term, Transp. Theory and Stat. Phys., 14 (1985), pp. 291-322. | MR | Zbl

[7] C.P. Grünfeld, Global solutions to a mixed problem for the Boltzmann equation with Lorentz force term, Transp. Theory Stat. Phys., 15 (1986), pp. 529-549. | MR | Zbl

[8] T. Kato, Perturbation Theory for Linear Operators, Springer, New York (1976). | MR | Zbl

[9] 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), pp. 984-996. | MR | Zbl

[10] A. Palczewski, A time dependent linear Boltzmann operator as the generator of a semigroup, Bull. Acad. Polon. Sci. Ser. Sci. Tech., 25 (1977), pp. 233-237. | MR | Zbl

[11] A. Palczewski, Spectral properties of the space nonhomogeneous linearized Boltzmann operator, Transp. Theory Stat. Phys., 13 (1984), pp. 409-430. | MR | Zbl

[12] M. Reed - B. Simon, Methods of Mathematical Physics, Vol. I, Functional Analysis, Academic Press, New York (1980). | MR | Zbl

[13] M. Reed - B. Simon, Methods of Mathematical Physics, Vol. IV, Analysis of Operators, Academic Press, New York (1978). | MR | Zbl

[14] M. Tabata, Decay of solutions to the mixed problem with the periodicity boundary condition for the linearized Boltzmann equation with conservative external force, Comm. Partial Differential Equations, 18 (1993), pp. 1823-1846. | MR | Zbl

[15] 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), pp. 741-780. | MR | Zbl

[16] M. Wing, An Introduction to Transport Theory, J. Wiley and Sons, New York (1962). | MR

[17] B. Wennberg, Stability and exponential convergence for the Boltzmann equation, Doctoral Thesis. Göteborg University.