Vladislav Panferov: Research

Research

My research interests belong broadly to the area which connects microscopic (atomistic) description of matter with continuum (hydrodynamic) descriptions. I particularly work on kinetic equations (Boltzmann, Vlasov...) studying the questions of well-posedness, formation of singularities and mathematical validation of various models. I am also interested in applications of these models in biology, physics and other natural sciences.

Papers and preprints:

L. Chayes, V. Panferov; The McKean-Vlasov equation in finite volume, J. Stat. Phys. 138 (2010), no. 1-3, 351-380. paper available through SpringerLink.
J. A. Carrillo, M. R. D'Orsogna, V. Panferov; Double milling in self-propelled swarms from kinetic theory, Kinet. Relat. Models 2 (2009), no. 2, 363-378. paper available from KRM.
A. Biryuk, W. Craig, V. Panferov; Strong solutions of the Boltzmann equation in one spatial dimension, C. R. Math. Acad. Sci. Paris 342 (2006), no. 11, 843--848., preprint PDF
I. M. Gamba, V. Panferov and C. Villani; Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation, Arch. Ration. Mech. Anal. 194 (2009), no. 1, 253-282; preprint PDF.
M. Herty, R. Illner, A. Klar, V. Panferov; On the qualitative properties of the systems of Fokker-Planck equations for multilane traffic flows, Transport Theory Statist. Phys. 35 (2006), no. 1-2, 31-54. paper: PDF
A. V. Bobylev, I. M. Gamba and V. Panferov; Moment inequalities and high-energy tails for the Boltzmann equations with inelastic interactions, Journ. Stat. Phys. vol. 116, no. 5-6 pp. 1651--1682 (2004), preprint available from ArXiv.org; paper available from the journal.
I. M. Gamba, V. Panferov and C. Villani; On the Boltzmann equation for diffusively excited granular media; Comm. Math. Phys. 246, no. 3, pp. 503-541 (2004); preprint available from ArXiv.org; paper available from CMP.
I. M. Gamba, V. Panferov and C. Villani; On the inelastic Boltzmann equation with diffusive forcing. Nonlinear problems in mathematical physics and related topics, II, 179--192, Int. Math. Ser. (N. Y.), 2, Kluwer/Plenum, New York, 2002.
V. Panferov, On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004), no. 4, 771--825. preprint version: Postscript, PDF.
V. Panferov and A. Heintz; A new discrete-velocity model for the Boltzmann equation, Math. Methods Appl. Sci. 25 (2002), no. 7, 571--593. preprint: Postscript, PDF; full text of the paper available from Wiley Interscience (access required)