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On the Computation of the Spectrum of the Linearized Boltzmann Collision Operator for Maxwellian Molecules

Emanuele Dolera

Bollettino dell'Unione Matematica Italiana (2011)

  • Volume: 4, Issue: 1, page 47-68
  • ISSN: 0392-4041

Abstract

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In this article we provide a complete and self-contained treatment of the spectrum of the linearized Boltzmann collision operator for Maxwellian molecules.

How to cite

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Dolera, Emanuele. "On the Computation of the Spectrum of the Linearized Boltzmann Collision Operator for Maxwellian Molecules." Bollettino dell'Unione Matematica Italiana 4.1 (2011): 47-68. <http://eudml.org/doc/290712>.

@article{Dolera2011,
abstract = {In this article we provide a complete and self-contained treatment of the spectrum of the linearized Boltzmann collision operator for Maxwellian molecules.},
author = {Dolera, Emanuele},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {47-68},
publisher = {Unione Matematica Italiana},
title = {On the Computation of the Spectrum of the Linearized Boltzmann Collision Operator for Maxwellian Molecules},
url = {http://eudml.org/doc/290712},
volume = {4},
year = {2011},
}

TY - JOUR
AU - Dolera, Emanuele
TI - On the Computation of the Spectrum of the Linearized Boltzmann Collision Operator for Maxwellian Molecules
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/2//
PB - Unione Matematica Italiana
VL - 4
IS - 1
SP - 47
EP - 68
AB - In this article we provide a complete and self-contained treatment of the spectrum of the linearized Boltzmann collision operator for Maxwellian molecules.
LA - eng
UR - http://eudml.org/doc/290712
ER -

References

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  2. CARLEN, E. A. - LU, X., Fast and slow convergence to equilibrium for Maxwellian molecules via Wild Sums. J. Stat. Phys., 112 (2003), 59-134. Zbl1079.82012MR1991033DOI10.1023/A:1023623503092
  3. CERCIGNANI, C., Mathematical Methods in Kinetic Theory. Plenum Press, New York (1969). Zbl0191.25103MR255199
  4. CERCIGNANI, C., The Boltzmann Equation and its Applications. Springer-Verlag, New York (1988). Zbl0646.76001MR1313028DOI10.1007/978-1-4612-1039-9
  5. CERCIGNANI, C. - LAMPIS, M. - SGARRA, C., L 2 -Stability near equilibrium of the solution of the homogeneous Boltzmann equation in the case of Maxwellian molecules. Meccanica, 23 (1988), 15-18. Zbl0667.76119MR980181DOI10.1007/BF01561005
  6. CHAPMAN, S. - COWLING, T. G., The Mathematical Theory of Nonuniform Gases. 1st ed. Cambridge University Press, Cambridge (1939). Zbl0063.00782MR1148892
  7. ERDÉLYI, A. - MAGNUS, W. - OBERHETTINGER, F. - TRICOMI, F. G., Higher trascendental functions. McGraw Hill, New York (1953). 
  8. GRAD, H., Asymptotic theory of the Boltzmann equation, II. Rarefied Gas Dynamics, 3rd Symposium (1962), 26-59. MR156656
  9. HILBERT, D., Begründung der kinetischen Gastheorie. Math. Ann., 72 (1912), 562-577. MR1511713DOI10.1007/BF01456676
  10. MOUHOT, C., Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials. Comm. Math. Phys., 261 (2006), 629-672. Zbl1113.82062MR2197542DOI10.1007/s00220-005-1455-x
  11. MOUHOT, C., Quantitative linearized study of the Boltzmann collision operator and applications. Commun. Math. Sci., 5, suppl. 1 (2007), 73-86. Zbl1219.76045MR2301289DOI10.4310/CMS.2007.v5.n5.a6
  12. PRUDNIKOV, A. P. - BRYCHKOV, YU. A. - MARICHEV, O. I., Integrals and Series. Vol. 4: Laplace Transforms. Gordon and Breach Science Publishers, Amsterdam (1998). MR1162979
  13. SANSONE, G., Orthogonal Functions. Pure and Applied Mathematics. Vol. IX (1959). Interscience Publishers, New York. Reprinted by Dover Publications (1991). MR103368
  14. TRUESDELL, C. - MUNCASTER, R., Fundamentals of Maxwell's Kinetic Theory of a Simple Monoatomic Gas. Academic Press, New York (1980). MR554086
  15. VILLANI, C., A review of mathematical topics in collisional kinetic theory. Handbook of Mathematical Fluid Dynamics, Vol. I (2002), 71-305. (S. Friedlander and D. Serre eds.). North-Holland, Amsterdam. Zbl1170.82369MR1942465DOI10.1016/S1874-5792(02)80004-0
  16. WANG CHANG, C. S. - UHLENBECK, G. E., On the propagation of sound in monoatomic gases. Univ. of Michigan Press. Ann Arbor, Michigan. Reprinted in 1970 in Studies in Statistical Mechanics. Vol. V (1952). Edited by J. L. Lebowitz - E. Montroll, North-Holland. 
  17. WATSON, G. N., A Treatise on the Thery of Bessel Functions. 2nd ed. Cambridge University Press, London (1944). MR10746

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