Decay of solutions to the mixed problem for the linearized Boltzmann equation with a potential term in a polyhedral bounded domain
Rendiconti del Seminario Matematico della Università di Padova, Volume 103 (2000), pp. 133-155.
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     author = {Tabata, Minoru and Eshima, Nobuoki},
     title = {Decay of solutions to the mixed problem for the linearized {Boltzmann} equation with a potential term in a polyhedral bounded domain},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {133--155},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {103},
     year = {2000},
     mrnumber = {1789535},
     zbl = {0982.45006},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2000__103__133_0/}
}
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Tabata, Minoru; Eshima, Nobuoki. Decay of solutions to the mixed problem for the linearized Boltzmann equation with a potential term in a polyhedral bounded domain. Rendiconti del Seminario Matematico della Università di Padova, Volume 103 (2000), pp. 133-155. http://www.numdam.org/item/RSMUP_2000__103__133_0/

[1] 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

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

[3] N. Bellomo, M. Lachowicz, A. Palczewski AND G. Toscani, On the initial value problem for the Boltzmann equation with a force term, Transp. Theory Stat. Phys., 18, 1 (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] H. Grad, Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, Proc. Symp. in Appl. Math., 17 (1965), pp. 154-183. [7] C.P. Grünfeld, On the nonlinear Boltzmann equation with force term, Transp. Theory Stat. Phys., 14, 3 (1985), pp. 291-322. | MR | Zbl

[8] C.P. Grünfeld, Global solution to a mixed problem for the Boltzmann equation with Lorentz force term, Transp. Theory Stat. Phys., 15, 4 (1986), pp. 529-549. | 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. 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 Differ. Eqs., 18, 11 (1993), pp. 1823-1846. | MR | Zbl

[13] 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, 6 (1994), pp. 741-780. | MR | Zbl

[14] M. Tabata, The point spectrum of the linearized Boltzmann operator with an external-force potential in an exterior domain, Transp. Theory Stat. Phys., 24, 9 (1995), pp. 1271-1294. | MR | Zbl

[15] M. Tabata - N. Eshima, The point spectrum of the linearized Boltzmann operator with the potential term in a semi-infinite domain and the corresponding eigenspaces, Rendiconti Sem. Mat. Univ. Politecnico di Torino, 53, 2 (1995), pp. 29-38. | MR | Zbl

[16] M. Tabata - N. Eshima, The spectrum of the transport operator with a potential term under the spatial periodicity condition, Rendiconti Sem. Mat. Univ. Padova, 97 (1997), pp. 211-233. | Numdam | MR | Zbl

[17] B. Wennberg, Stability and exponential convergence for the Boltzmann equation, Doctoral Thesis, Götteborg University (1993). | Zbl