相关论文: A Bhatnagar-Gross-Krook Approximation to Stochasti…
Scalar conservation laws sit at the intersection between being simple enough to study analytically, while being complex enough to exhibit a wide range of nonlinear phenomena. We introduce a novel stochastic perturbation of scalar…
We study the BGK approximation to first-order scalar conservation laws with a flux which is discontinuous in the space variable. We show that the Cauchy Problem for the BGK approximation is well-posed and that, as the relaxation parameter…
We study compactness properties of time-discrete and continuous time BGK-type schemes for scalar conservation laws, in which microscopic interactions occur only when the state of a system deviates significantly from an equilibrium…
We study the derivation of a scalar conservation law with stochastic forcing starting from a stochastic BGK model with a high-field scaling. We prove the convergence to a new kinetic formulation where appears a modified Maxwellian. We…
This work is devoted to examine the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator and a multiplicative noise. Our proof for uniqueness is based…
Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these…
We propose, study, and compute solutions to a class of optimal control problems for hyperbolic systems of conservation laws and their viscous regularization. We take barotropic compressible Navier--Stokes equations (BNS) as a canonical…
In this paper we study a non strictly systems of conservation law by stochastic perturbation. We show the existence and uniqueness of the solution. We do not assume that $BV$-regularity for the initial conditions. The proofs are based on…
In this work we study variational properties of approximate solutions of scalar conservation laws. Solutions of this type are described by a kinetic equation which is similar to the kinetic representation of admissible weak solutions due to…
This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in…
We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well-posed: it admits a unique solution, characterized by a kinetic formulation…
In this paper we study the hydrodynamic limit of a B.G.K. like kinetic model on domains with boundaries via $BV_{loc}$ theory. We obtain as a consequence existence results for scalar multidimensional conservation laws with kinetic boundary…
In this paper, we establish a small time large deviation principles for scalar stochastic conservation laws driven by multiplicative noise. The doubling of variables method plays a key role.
A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice…
We develop a general framework for the analysis of approximations to stochastic scalar conservation laws. Our aim is to prove, under minimal consistency properties and bounds, that such approximations are converging to the solution to a…
The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is small. In practice, however, Knudsen layers emerge at the…
In this paper, we consider the Cauchy problem for the nonlinear fractional conservation laws driven by a multiplicative noise. In particular, we are concerned with the well-posedness theory and the study of the long-time behavior of…
A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…
Bhatnagar-Gross-Krook (BGK) equation is a relaxation model of the Boltzmann equation which is widely used in place of the Boltzmann equation for the simulation of various kinetic flow problems. In this work, we study the asymptotic…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…