We overview some recent results in the field of uncertainty quantification for kinetic
equations and related problems with random inputs. Uncertainties may be due to various …

In this paper, we study the multiscale Boltzmann equation with multi-dimensional random
parameters by a bi-fidelity stochastic collocation (SC) method developed in [52],[70],[71]. By …

We consider a kinetic model for a two component gas mixture without chemical reactions.
Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in …

In [L. Liu and S. **, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence
and long-time decay of the numerical solution towards the global equilibrium of the …

In this paper, we conduct uniform error estimates of the bifidelity method for multiscale
kinetic equations. We take the Boltzmann and the linear transport equations as important …

In this paper the nonlinear multi-species Boltzmann equation with random uncertainty
coming from the initial data and collision kernel is studied. Well-posedness and long-time …

In this paper, we consider the high order method for solving the linear transport equations
under diffusive scaling and with random inputs. To tackle the randomness in the problem …

There have been many challenges in studying multiscale kinetic models with uncertainties.
Quantifying uncertainties in the models such as arisen from collision kernels, initial or …

We study uncertainty quantification for a Boltzmann-Poisson system that models electron
transport in semiconductors and the physical collision mechanisms over the charges, using …