Keywords: Granular gases, Kinetic models, Boltzmann equation

@article{AIHPC_2010__27_2_719_0, author = {Furioli, G. and Pulvirenti, A. and Terraneo, E. and Toscani, G.}, title = {Convergence to self-similarity for the Boltzmann equation for strongly inelastic Maxwell molecules}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, publisher = {Elsevier}, volume = {27}, number = {2}, year = {2010}, pages = {719-737}, doi = {10.1016/j.anihpc.2009.11.005}, zbl = {05690778}, mrnumber = {2595198}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2010__27_2_719_0} }

Furioli, G.; Pulvirenti, A.; Terraneo, E.; Toscani, G. Convergence to self-similarity for the Boltzmann equation for strongly inelastic Maxwell molecules. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 2, pp. 719-737. doi : 10.1016/j.anihpc.2009.11.005. http://www.numdam.org/item/AIHPC_2010__27_2_719_0/

[1] Self-similarity in random collision processes, Phys. Rev. E 68 (2003)

, , , ,[2] Decay rates in probability metrics towards homogeneous cooling states for the inelastic Maxwell model, J. Statist. Phys. 124 no. 2–4 (2006), 625-653 | MR 2264621 | Zbl 1135.82028

, , ,[3] Asymptotics of the fast diffusion equation via entropy estimates, Arch. Rational Mech. Anal. 191 (2009), 347-385 | MR 2481073 | Zbl 1178.35214

, , , , ,[4] The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules, Mathematical Physics Reviews, vol. 7, Soviet Sci. Rev. Sect. C Math. Phys. Rev. vol. 7, Harwood Academic Publ., Chur (1988), 111-233 | MR 1128328 | Zbl 0850.76619

,[5] Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions, J. Statist. Phys. 110 no. 1–2 (2003), 333-375 | MR 1966332 | Zbl 1134.82324

, ,[6] On some properties of kinetic and hydrodynamic equations for inelastic interactions, J. Statist. Phys. 98 no. 3–4 (2000), 743-773 | MR 1749231 | Zbl 1056.76071

, , ,[7] Generalized kinetic Maxwell type models of granular gases, Mathematical Models of Granular Matter, Lecture Notes in Math. vol. 1937, Springer, Berlin (2008), 23-57 | MR 2436467 | Zbl 1298.76209

, , ,[8] Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, J. Statist. Phys. 111 no. 1–2 (2003), 403-417 | MR 1964277 | Zbl 1119.82318

, , ,[9] Tanaka theorem for inelastic Maxwell models, Comm. Math. Phys. 276 no. 2 (2007), 287-314 | MR 2346391 | Zbl 1136.82033

, ,[10] Kinetic approach to long time behavior of linearized fast diffusion equations, J. Statist. Phys. 128 no. 4 (2007), 883-925 | MR 2344717 | Zbl 1131.82030

, ,[11] Strong convergence towards homogeneous cooling states for dissipative Maxwell models, Annales IHP Non Linear Analysis 26 no. 5 (2009), 1675-1700 | Numdam | MR 2566705 | Zbl 1175.82046

, , ,[12] Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas, Comm. Math. Phys. 199 no. 3 (1999), 521-546 | MR 1669689 | Zbl 0927.76088

, , ,[13] Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates, Rev. Mat. Iberoamericana 19 (2003), 1-48 | MR 2053570 | Zbl 1073.35127

, , ,[14] Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch. Rational Mech. Anal. 179 (2006), 217-263 | MR 2209130 | Zbl 1082.76105

, , ,[15] Asymptotic ${L}^{1}$-decay of solutions of the porous medium equation to self-similarity, Indiana Univ. Math. J. 49 no. 1 (2000), 113-142 | MR 1777035 | Zbl 0963.35098

, ,[16] Contractive probability metrics and asymptotic behavior of dissipative kinetic equations, Riv. Mat. Univ. Parma (7) 6 (2007), 75-198 | MR 2355628 | Zbl 1142.82018

, ,[17] Propagation of Gevrey regularity for solutions of the Boltzmann equation for Maxwellian molecules, Trans. Amer. Math. Soc. 361 (2009), 1731-1747 | MR 2465814 | Zbl 1159.76044

, , ,[18] Strong convergence towards self-similarity for one-dimensional dissipative Maxwell models, J. Funct. Anal. 257 no. 7 (2009), 2291-2324 | MR 2548036 | Zbl 1180.82150

, , , ,[19] On the Boltzmann equation for diffusively excited granular media, Comm. Math. Phys. 246 no. 3 (2004), 503-541 | MR 2053942 | Zbl 1106.82031

, , ,[20] A strengthened central limit theorem for smooth densities, J. Funct. Anal. 129 no. 1 (1995), 148-167 | MR 1322646 | Zbl 0822.60018

, ,[21] Topics in Mass Transportation, Grad. Stud. Math. vol. 58 (2003)

,[22] Mathematics of granular materials, J. Statist. Phys. 124 no. 2–4 (2006), 781-822 | MR 2264625 | Zbl 1134.82040

,