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

Dolera, Emanuele:
On the Computation of the Spectrum of the Linearized Boltzmann Collision Operator for Maxwellian Molecules
Bollettino dell'Unione Matematica Italiana Serie 9 4 (2011), fasc. n.1, p. 47-68, (English)
pdf (335 Kb), djvu (188 Kb). | MR 2797465 | Zbl 1251.82045

Sunto

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

Referenze Bibliografiche

[1] A. V. BOBYLEV, The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules. Mathematical Physics Reviews, 7 (1988), 111-233. | MR 1128328 | Zbl 0850.76619

[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. | fulltext (doi) | MR 1991033 | Zbl 1079.82012

[3] C. CERCIGNANI, Mathematical Methods in Kinetic Theory. Plenum Press, New York (1969). | MR 255199 | Zbl 0191.25103

[4] C. CERCIGNANI, The Boltzmann Equation and its Applications. Springer-Verlag, New York (1988). | fulltext (doi) | MR 1313028 | Zbl 0646.76001

[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. | fulltext (doi) | MR 980181 | Zbl 0667.76119

[6] S. CHAPMAN - T. G. COWLING, The Mathematical Theory of Nonuniform Gases. 1st ed. Cambridge University Press, Cambridge (1939). | MR 1148892 | Zbl 0063.00782

[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 156656

[9] D. HILBERT, Begründung der kinetischen Gastheorie. Math. Ann., 72 (1912), 562-577. | fulltext EuDML | fulltext (doi) | MR 1511713

[10] C. MOUHOT, Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials. Comm. Math. Phys., 261 (2006), 629-672. | fulltext (doi) | MR 2197542 | Zbl 1113.82062

[11] C. MOUHOT, Quantitative linearized study of the Boltzmann collision operator and applications. Commun. Math. Sci., 5, suppl. 1 (2007), 73-86. | fulltext (doi) | MR 2301289 | Zbl 1219.76045

[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 1162979

[13] G. SANSONE, Orthogonal Functions. Pure and Applied Mathematics. Vol. IX (1959). Interscience Publishers, New York. Reprinted by Dover Publications (1991). | MR 103368

[14] C. TRUESDELL - R. MUNCASTER, Fundamentals of Maxwell's Kinetic Theory of a Simple Monoatomic Gas. Academic Press, New York (1980). | MR 554086

[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. | fulltext (doi) | MR 1942465 | Zbl 1170.82369

[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 10746

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche