[INS COLLOQUIUM] On a class of self-similar solutions of the Boltzmann equation

We consider the nonlinear Boltzmann equation and discuss various classes of its self-similar solutions. Some of them were investigated in joint works of the author with Carlo Cercignani (and also with Irene Gamba) in 2000s. This work can be considered as a development of some ideas of that time. In particular, we consider the class of so-called affine homoenergetic flows and their generalizations. For the case of pseudo-Maxwell molecules we give a constructive proof of existence and uniqueness of self-similar solutions and show that these solutions are attractors for certain classes of initial conditions. The lecture is partly based on a recent joint paper [1] with Alessia Nota and Juan Velazquez.

[1] Bobylev A.V., Nota A. and Velazquez J. L., Self-similar asymptotics for a modified Maxwell-Boltzmann equation in systems subject to deformations. Commun. Math. Phys., 380 (2020), 409 – 448. https://doi.org/10.1007//s00220-020-03858-2

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BIO
Prof. Alexander Bobylev is currently a Chief Scientist at Keldysh Institute of Applied Mathematics, Academy of Sciences of Russia, Moscow. He got PhD in Mathematics in 1978 and the Doctor of Sciences (Dr. Hab.) degree in 1984 at the Keldysh Institute of Appl. Math., USSR Academy of Sciences. In 1999 - 2014 he has been working as a professor of Karlstad University (Sweden) and was a member of the Board of Swedish National School in Mathematics and Scientific Computing (FMB, Uppsala). He has been received several professional distinctions, awarded USSR State Prize in Science and Technology in 1989, Honorary Degree (Dottore ad Honorem) from Parma University in 1998, 100 Anniversary Chalmers Visiting Professor in 1999, “Best Paper of the Year 2000” from Japan Society of Fluid Mechanics in 2001, etc. He has given the Harold Grad Lecture at 25th Int. Symposium on Rarefied Gas Dynamics, Saint-Petersburg (Russia), 2006.

He acts as a member of Editorial Board of the journals, Journal of Statistical Physics (2007 - 2013) and Kinetic and Related Models. At the same time, he is a member of International Advisory Board of the journal Rivista di Matematica della Universita di Parma (since 2009) and member of the Board of Honor of International Symposium in Rarefied Gas Dynamics (since 2010). Roughly he has published 130 research publications including two books (“Exact and Approximate Methods in the Theory of Boltzmann and Landau Kinetic Equations” (in Russian), KIAM, Moscow, 1987, and “Kinetic Equations, Volume 1: Boltzmann Equation, Maxwell Models and Hydrodynamics beyond Navier-Stokes”, De Gruyter Series in Applied and Numerical Mathematics 5/1, De Gruyter, Berlin/Boston, 2020).