相关论文: A Bhatnagar-Gross-Krook Approximation to Stochasti…

One proves here the backward uniqueness of solutions to stochastic semilinear parabolic equations and also for the tamed Navier-Stokes equations driven by linearly multiplicative Gaussian noises. Applications to approximate controllability…

Due to limited possibilities of experimental investigations for non-equilibrium gas flows, numerical results are of highest interest. Although the well-established Direct Simulation Monte Carlo (DSMC) method achieves highly accurate…

We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential-type approximation of the Dirac distribution. This enables…

The Bhatnagar-Gross-Krook (BGK) model as well as its extensions (ellipsoidal statistical BGK, Shakhov BGK, unified BGK) are used in particle-based fluid dynamics and compared with the Direct Simulation Monte Carlo (DSMC) method. To this…

The spatially homogeneous BGK equation is obtained as the limit if a model of a many particle system, similar to Mark Kac's charicature of the spatially homogeneous Boltzmann equation.

We explore numerical approximation of multidimensional stochastic balance laws driven by multiplicative L\'{e}vy noise via flux- splitting finite volume method. The convergence of the approximations is proved towards the unique entropy…

We formulate an initial- and Dirichlet boundary- value problem for a linear stochastic heat equation, in one space dimension, forced by an additive space-time white noise. First, we approximate the mild solution to the problem by the…

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…

We consider a semi-discrete finite volume scheme for a degenerate fractional conservation laws driven by a cylindrical Wiener process. Making use of the bounded variation (BV) estimates, Young measure theory, and a clever adaptation of…

We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…

We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…

In this paper, we present a new class of conservative semi-Lagrangian schemes for kinetic equations. They are based on the conservative reconstruction technique introduced in [S. Y. Cho, et al., Conservative semi-Lagrangian schemes for…

In this paper, we established the Freidlin-Wentzell type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the…

We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose…

We propose a BGK-type kinetic model for relativistic reactive gas mixtures. This model serves as a computationally tractable yet physically consistent alternative to the corresponding Boltzmann equation. The relaxation operator is…

Using small noise limit approach, we study degenerate stochastic ergodic control problems and as a byproduct obtain error bounds for the $\varepsilon$-optimal controls. We also establish tunneling for a special ergodic control problem and…

We consider in this paper a velocity discretized version of the full linear kinetic BGK model and the corresponding limit for small Knudsen number, the linearised Euler or acoustic system. Considering these equations on networks, coupling…

In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. Under the assumption that the rarefaction curve of…

This paper is concerned with the development of suitable numerical method for the approximation of discontinuous solutions of parameter-dependent linear hyperbolic conservation laws. The objective is to reconstruct such approximation, for…

We present some recent developments on shock capturing methods for nonlinear hyperbolic systems of balance laws, whose prototype is the Euler system of compressible fluid flows, and especially discuss {structure-preserving} techniques. The…