Related papers: Boltzmann equation with mixed boundary condition
In this article, we study the stationary Boltzmann equation with the incoming boundary condition for the hard potential cases. Assuming the smallness of the domain and a suitable normal curvature condition on the boundary, we find a…
We study the dynamics of an interacting classical gas trapped in a double-well potential at finite temperature. Two model potentials are considered: a cubic box with a square barrier in the middle, and a harmonic trap with a gaussian…
The two-dimensional, periodic Lorentz gas, is the dynamical system corresponding with the free motion of a point particle in a planar system of fixed circular obstacles centered at the vertices of a square lattice in the Euclidian plane.…
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…
We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
We construct a unique global-in-time solution to the two species Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition, which can be viewed as one of the ideal scattering boundary model. The construction…
In the present work the linearized problem of plasma wave reflection from a boundary of a half--space is solved analytically. Specular accommodative conditions of plasma wave reflection from plasma boundary are taken into consideration.…
An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…
We investigate singularly perturbed elliptic problems with multiplicative nonlocal diffusion terms subject to Robin boundary conditions. The diffusion depends on a global quantity of the solution, which introduces a nonlocal coupling…
We study the long-time dynamics of the time-evolutionary Boltzmann equation with hard sphere collisions in the three-dimensional half-space \( \mathbb{R}^2 \times \mathbb{R}^+\), subject to diffuse reflection boundary conditions and small…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
Lattice Boltzmann models provide better understanding with mesoscopic eyesight on multi-component diffusion than macroscopic models. Based on the kinetic theory and starting from the He-Luo model, the state-of-the-art multi-component…
The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…
The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is…
We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some…
We propose a necessary and sufficient condition for the well-posedness of the linear non-homogeneous Grad moment equations in half-space. The Grad moment system is based on Hermite expansion and regarded as an efficient reduction model of…
Homo-energetic solutions to the spatially homogeneous Boltzmann equation have been extensively studied, but their global stability in the inhomogeneous setting remains challenging due to unbounded energy growth under self-similar scaling…
The Boltzmann equation for inelastic Maxwell models is used to analyze nonlinear transport in a granular binary mixture in the steady simple shear flow. Two different transport processes are studied. First, the rheological properties (shear…
While weak diffusive limit from the Boltzmann equation to the incompressible Navier-Stokes-Fourier system was established for the Maxwell boundary condition within renormalized solutions framework [Saint.Raymond2009][Jiang-Masmoudi2017],…
A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167--247) via an energetic variational approach.…