Decay of solutions to the mixed problem for the linearized Boltzmann equation with a potential term in a polyhedral bounded domain
Tabata, Minoru ; Eshima, Nobuoki
Rendiconti del Seminario Matematico della Università di Padova, Tome 104 (2000), p. 133-155 / Harvested from Numdam
Publié le : 2000-01-01
@article{RSMUP_2000__103__133_0,
     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},
     volume = {104},
     year = {2000},
     pages = {133-155},
     mrnumber = {1789535},
     zbl = {0982.45006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2000__103__133_0}
}
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, Tome 104 (2000) pp. 133-155. http://gdmltest.u-ga.fr/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 629561

[2] R. Beals - V. PROTOPOPESCU, Abstract time-dependent transport equations, J. Math. Anal. Appl., 121 (1987), pp. 370-405. | MR 872231 | Zbl 0657.45007

[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 1006668 | Zbl 0699.35237

[4] H.B. Drange, On the Boltzmann equation with external forces, SIAM J. Appl. Math., 34 (1978), pp. 577-592. | MR 479244 | Zbl 0397.76068

[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 156656

[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 184507 | Zbl 0144.48203

[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 861407 | Zbl 0631.76091

[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 436842 | Zbl 0367.76068

[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 459453 | Zbl 0363.45009

[11] A. Palczewski, Spectral properties of the space nonhomogeneous linearized Boltzmann operator, Transp. Theory Stat. Phys., 13 (1984), pp. 409-430. | MR 759864 | Zbl 0585.47023

[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 1243527 | Zbl 0798.35146

[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 1279588 | Zbl 0817.35116

[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 1362330 | Zbl 0871.76080

[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 1375405 | Zbl 0841.76079

[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 1476172 | Zbl 0887.45004

[17] B. Wennberg, Stability and exponential convergence for the Boltzmann equation, Doctoral Thesis, Götteborg University (1993). | Zbl 0828.76076