On the Computation of the Spectrum of the Linearized Boltzmann Collision Operator for Maxwellian Molecules
Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 1, pp. 47-68.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this article we provide a complete and self-contained treatment of the spectrum of the linearized Boltzmann collision operator for Maxwellian molecules.
@article{BUMI_2011_9_4_1_a2,
     author = {Dolera, Emanuele},
     title = {On the {Computation} of the {Spectrum} of the {Linearized} {Boltzmann} {Collision} {Operator} for {Maxwellian} {Molecules}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {47--68},
     publisher = {mathdoc},
     volume = {Ser. 9, 4},
     number = {1},
     year = {2011},
     zbl = {1251.82045},
     mrnumber = {2797465},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_1_a2/}
}
TY  - JOUR
AU  - Dolera, Emanuele
TI  - On the Computation of the Spectrum of the Linearized Boltzmann Collision Operator for Maxwellian Molecules
JO  - Bollettino della Unione matematica italiana
PY  - 2011
SP  - 47
EP  - 68
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_1_a2/
LA  - en
ID  - BUMI_2011_9_4_1_a2
ER  - 
%0 Journal Article
%A Dolera, Emanuele
%T On the Computation of the Spectrum of the Linearized Boltzmann Collision Operator for Maxwellian Molecules
%J Bollettino della Unione matematica italiana
%D 2011
%P 47-68
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_1_a2/
%G en
%F BUMI_2011_9_4_1_a2
Dolera, Emanuele. On the Computation of the Spectrum of the Linearized Boltzmann Collision Operator for Maxwellian Molecules. Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 1, pp. 47-68. http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_1_a2/

[1] A. V. Bobylev, The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules. Mathematical Physics Reviews, 7 (1988), 111-233. | MR | Zbl

[2] E. A. Carlen - X. Lu, Fast and slow convergence to equilibrium for Maxwellian molecules via Wild Sums. J. Stat. Phys., 112 (2003), 59-134. | DOI | MR | Zbl

[3] C. Cercignani, Mathematical Methods in Kinetic Theory. Plenum Press, New York (1969). | MR | Zbl

[4] C. Cercignani, The Boltzmann Equation and its Applications. Springer-Verlag, New York (1988). | DOI | MR | Zbl

[5] C. Cercignani - M. Lampis - C. Sgarra, $L^2$-Stability near equilibrium of the solution of the homogeneous Boltzmann equation in the case of Maxwellian molecules. Meccanica, 23 (1988), 15-18. | DOI | MR | Zbl

[6] S. Chapman - T. G. Cowling, The Mathematical Theory of Nonuniform Gases. 1st ed. Cambridge University Press, Cambridge (1939). | MR | Zbl

[7] A. Erdélyi - W. Magnus - F. Oberhettinger - F. G. Tricomi, Higher trascendental functions. McGraw Hill, New York (1953).

[8] H. Grad, Asymptotic theory of the Boltzmann equation, II. Rarefied Gas Dynamics, 3rd Symposium (1962), 26-59. | MR

[9] D. Hilbert, Begründung der kinetischen Gastheorie. Math. Ann., 72 (1912), 562-577. | fulltext EuDML | DOI | MR

[10] C. Mouhot, Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials. Comm. Math. Phys., 261 (2006), 629-672. | DOI | MR | Zbl

[11] C. Mouhot, Quantitative linearized study of the Boltzmann collision operator and applications. Commun. Math. Sci., 5, suppl. 1 (2007), 73-86. | DOI | MR | Zbl

[12] A. P. Prudnikov - Yu. A. Brychkov - O. I. Marichev, Integrals and Series. Vol. 4: Laplace Transforms. Gordon and Breach Science Publishers, Amsterdam (1998). | MR

[13] G. Sansone, Orthogonal Functions. Pure and Applied Mathematics. Vol. IX (1959). Interscience Publishers, New York. Reprinted by Dover Publications (1991). | MR

[14] C. Truesdell - R. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monoatomic Gas. Academic Press, New York (1980). | MR

[15] C. Villani, 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. | DOI | MR | Zbl

[16] C. S. Wang Chang - G. E. Uhlenbeck, 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] G. N. Watson, A Treatise on the Thery of Bessel Functions. 2nd ed. Cambridge University Press, London (1944). | MR