The spectrum of the transport operator with a potential term under the spatial periodicity condition

Minoru Tabata; Nobuoki Eshima

Rendiconti del Seminario Matematico della Università di Padova (1997)

  • Volume: 97, page 211-233
  • ISSN: 0041-8994

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Tabata, Minoru, and 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 97 (1997): 211-233. <http://eudml.org/doc/108425>.

@article{Tabata1997,
author = {Tabata, Minoru, Eshima, Nobuoki},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {transport operator; spectrum; eigenvalues},
language = {eng},
pages = {211-233},
publisher = {Seminario Matematico of the University of Padua},
title = {The spectrum of the transport operator with a potential term under the spatial periodicity condition},
url = {http://eudml.org/doc/108425},
volume = {97},
year = {1997},
}

TY - JOUR
AU - Tabata, Minoru
AU - Eshima, Nobuoki
TI - The spectrum of the transport operator with a potential term under the spatial periodicity condition
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1997
PB - Seminario Matematico of the University of Padua
VL - 97
SP - 211
EP - 233
LA - eng
KW - transport operator; spectrum; eigenvalues
UR - http://eudml.org/doc/108425
ER -

References

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  1. [1] R. Beals - V. PROTOPOPESCU, Abstract time-dependent transport equations, J. Math. Anal. Appl., 121 (1987), pp. 370-405. Zbl0657.45007MR872231
  2. [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. MR629561
  3. [3] N. Bellomo - M. LACHOWICZ - A. PALCZEWSKI - G. TOSCANI, On the initial value problem for the Boltzmann equation with a force term, Transp. TheoryStat. Phys., 18 (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] C.P. Grünfeld, On the nonlinear Boltzmann equation with force term, Transp. Theory and Stat. Phys., 14 (1985), pp. 291-322. Zbl0609.76086MR798451
  7. [7] C.P. Grünfeld, Global solutions to a mixed problem for the Boltzmann equation with Lorentz force term, Transp. TheoryStat. Phys., 15 (1986), pp. 529-549. Zbl0631.76091MR861407
  8. [8] T. Kato, Perturbation Theory for Linear Operators, Springer, New York (1976). Zbl0148.12601MR407617
  9. [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
  10. [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
  11. [11] A. Palczewski, Spectral properties of the space nonhomogeneous linearized Boltzmann operator, Transp. TheoryStat. Phys., 13 (1984), pp. 409-430. Zbl0585.47023MR759864
  12. [12] M. Reed - B. Simon, Methods of Mathematical Physics, Vol. I, Functional Analysis, Academic Press, New York (1980). Zbl0242.46001MR751959
  13. [13] M. Reed - B. Simon, Methods of Mathematical Physics, Vol. IV, Analysis of Operators, Academic Press, New York (1978). Zbl0401.47001MR493421
  14. [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. Zbl0798.35146MR1243527
  15. [15] M. Tabata, Decay of solutions to the Cauchy problem for the linearized Boltzmann equation with an unbounded external-force potential, Transp. TheoryStat. Phys., 23 (1994), pp. 741-780. Zbl0817.35116MR1279588
  16. [16] M. Wing, AnIntroduction to Transport Theory, J. Wiley and Sons, New York (1962). MR155646
  17. [17] B. Wennberg, Stability and exponential convergence for the Boltzmann equation, Doctoral Thesis. Göteborg University. 

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