Page 476 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 476
CA18232: VARIATIONAL METHODS AND EQUATIONS ON GRAPHS (MS-40)
Nonlinear models of kinetic type: On the Cauchy problem and Banach
space regularity for Boltzmann flows of monatomic gas mixtures
Milana Pavic´ Cˇ olic´, milana.pavic@dmi.uns.ac.rs
Faculty of Sciences, University of Novi Sad, Serbia
Coauthors: Irene M. Gamba, Erica De La Canal
This talk will focus on the analysis of kinetic models for multi-component mixtures of monato-
mic gases with different masses. The model corresponds to a Boltzmann system for the evo-
lution of vector valued distribution function. The collision or interaction law, as much as the
modelling of the transition probability rates for pairwise interactions, are crucial components in
the dynamics.
We will present some recent rigorous results for the full non-linear space homogeneous
Boltzmann system of equations describing multi-component monatomic gas mixtures for binary
interactions. More precisely, we will show existence and uniqueness of the vector value solution
in the case of hard potentials and integrable angular scattering kernels associated to each pair
of interacting species, by means of an existence theorem for ODE systems in Banach spaces. In
addition, we will present several properties for such a solution, including integrability properties
of the multispecies collision operator. These properties together with a control by below imply
propagation of the polynomially and exponentially weighted Lp norms, 1 ≤ p ≤ ∞, associated
to the system solution. Additionally, for p = 1 we have generation of such moments.
Stochastic completeness of graphs: curvature and volume growth
Radoslaw Wojciechowski, rwojciechowski@gc.cuny.edu
York College and the Graduate Center, City University of New York, United States
We will summarize some recent work concerning stochastic completeness of graphs. In partic-
ular, we will discuss curvature criteria, uniqueness class and volume growth results.
474
Nonlinear models of kinetic type: On the Cauchy problem and Banach
space regularity for Boltzmann flows of monatomic gas mixtures
Milana Pavic´ Cˇ olic´, milana.pavic@dmi.uns.ac.rs
Faculty of Sciences, University of Novi Sad, Serbia
Coauthors: Irene M. Gamba, Erica De La Canal
This talk will focus on the analysis of kinetic models for multi-component mixtures of monato-
mic gases with different masses. The model corresponds to a Boltzmann system for the evo-
lution of vector valued distribution function. The collision or interaction law, as much as the
modelling of the transition probability rates for pairwise interactions, are crucial components in
the dynamics.
We will present some recent rigorous results for the full non-linear space homogeneous
Boltzmann system of equations describing multi-component monatomic gas mixtures for binary
interactions. More precisely, we will show existence and uniqueness of the vector value solution
in the case of hard potentials and integrable angular scattering kernels associated to each pair
of interacting species, by means of an existence theorem for ODE systems in Banach spaces. In
addition, we will present several properties for such a solution, including integrability properties
of the multispecies collision operator. These properties together with a control by below imply
propagation of the polynomially and exponentially weighted Lp norms, 1 ≤ p ≤ ∞, associated
to the system solution. Additionally, for p = 1 we have generation of such moments.
Stochastic completeness of graphs: curvature and volume growth
Radoslaw Wojciechowski, rwojciechowski@gc.cuny.edu
York College and the Graduate Center, City University of New York, United States
We will summarize some recent work concerning stochastic completeness of graphs. In partic-
ular, we will discuss curvature criteria, uniqueness class and volume growth results.
474
