相关论文: Higher-order Continuum Approximation for Rarefied …

We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous…

Maximum-entropy moment methods allow for the modelling of gases from the continuum regime to strongly rarefied conditions. The development of approximated solutions to the entropy maximization problem has made these methods computationally…

In this paper, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock wave in the flux approximation limit of Riemann solutions to the extended Chaplygin gas equations are analyzed and…

We derive an analytical connection between kinetic relaxation rate and bulk viscosity of a relativistic fluid in d spatial dimensions, all the way from the ultra-relativistic down to the near non-relativistic regime. Our derivation is based…

In this paper Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe…

In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK collision operator. Thanks to appropriate uniform estimates,…

We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…

This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…

One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum…

Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…

We compute exact second-order asymptotics for the cost of an optimal solution to the entropic optimal transport problem in the continuous-to-discrete, or semi-discrete, setting. In contrast to the discrete-discrete or continuous-continuous…

First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…

We consider a perturbation of a Hilbert space-valued Ornstein--Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts. The only further assumption on the drift is that it is bounded on balls…

This work investigates the long-time asymptotic behaviors of solutions to the initial value problem of the two-component nonlinear Klein-Gordon equation by inverse scattering transform and Riemann-Hilbert formulism. Two reflection…

In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ a…

A drift-diffusion model of miniband transport in strongly coupled superlattices is derived from the single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. We use a consistent Chapman-Enskog…

This work examines the idea of applying the Chapman-Enskog (CE) method for approximating the solution of the Boltzmann equation beyond the realm of physics, using an information theory approach. Equations describing the evolution of…

Classical convergence theory of Runge-Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff problems, that assumption is often violated, and a problematic…

Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…

Here we study the wave propagation and stability of general relativistic non-resistive dissipative second-order magnetohydrodynamic equations in curved space-time. We solve the Boltzmann equation for a system of particles and antiparticles…