Decay of solutions to the mixed problem for the linearized Boltzmann equation with a potential term in a polyhedral bounded domain

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1. [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. MR629561
2. [2] R. Beals - V. PROTOPOPESCU, Abstract time-dependent transport equations, J. Math. Anal. Appl., 121 (1987), pp. 370-405. Zbl0657.45007MR872231
3. [3] N. Bellomo, M. Lachowicz, A. Palczewski AND G. Toscani, On the initial value problem for the Boltzmann equation with a force term, Transp. TheoryStat. Phys., 18, 1 (1989), pp. 87-102. Zbl0699.35237MR1006668
4. [4] H.B. Drange, On the Boltzmann equation with external forces, SIAM J. Appl. Math., 34 (1978), pp. 577-592. Zbl0397.76068MR479244
5. [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. MR156656
6. [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. Zbl0144.48203MR184507
7. [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. Zbl0631.76091MR861407
8. [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. Zbl0367.76068MR436842
9. [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. Zbl0363.45009MR459453
10. [11] A. Palczewski, Spectral properties of the space nonhomogeneous linearized Boltzmann operator, Transp. TheoryStat. Phys., 13 (1984), pp. 409-430. Zbl0585.47023MR759864
11. [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. Zbl0798.35146MR1243527
12. [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. Zbl0817.35116MR1279588
13. [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. Zbl0871.76080MR1362330
14. [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. Zbl0841.76079MR1375405
15. [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. Zbl0887.45004MR1476172
16. [17] B. Wennberg, Stability and exponential convergence for the Boltzmann equation, Doctoral Thesis, Götteborg University (1993). Zbl0828.76076