相关论文: Boundary Layer of Transport Equation with In-Flow …

The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with…

Consider the unsteady neutron transport equation with diffusive boundary condition in 2D convex domains. We establish the diffusive limit with both initial layer and boundary layer corrections. The major difficulty is the lack of regularity…

Consider the steady neutron transport equation with diffusive boundary condition. In [Wu and Guo(2015) Comm. Math. Phys.] and [Wu and Yang and Guo(2016) Preprint], it was discovered that geometric correction is necessary for the Milne…

We consider the diffusive limit of an unsteady neutron transport equation in a two-dimensional plate with one-speed velocity. We show the solution can be approximated by the sum of interior solution, initial layer, and boundary layer with…

Consider the stationary Boltzmann equation in 2D convex domains with diffusive boundary condition. In this paper, we establish the hydrodynamic limits while the boundary layers are present, and derive the steady Navier-Stokes-Fourier system…

We consider the diffusive limit of a steady neutron transport equation with one-speed velocity in a two-dimensional annulus. A classical theorem states that the solution can be approximated in $L^{\infty}$ by the leading order interior…

Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish $W^{1,\infty}$ regularity for its solutions. Combined with a uniform $L^6$ estimate, such regularity leads to the validity…

Consider neutron transport equations in 3D convex domains with in-flow boundary. We mainly study the asymptotic limits as the Knudsen number $\epsilon\rightarrow 0^+$. Using Hilbert expansion, we rigorously justify that the solution of…

This paper considers the neutron transport equation in bounded domain with a combination of the diffusive boundary condition and the in-flow boundary condition. We firstly study the existence of solution in any fixed time by…

The rigorous justification of the hydrodynamic limits of kinetic equations in bounded domains has been actively investigated in recent years. In spite of the progress for the diffuse-reflection boundary case, the more challenging in-flow…

We revisit the diffusive limit of a steady neutron transport equation in a $2$-D unit disk with one-speed velocity. We show the classical result in [4] with Milne expansion is incorrect in $L^{\infty}$ and we give the right answer in…

Consider 3D Boltzmann equation in convex domains with diffusive-reflection boundary condition. We study the hydrodynamic limits as the Knudsen number and Strouhal number $\epsilon\rightarrow 0^+$. Using the Hilbert expansion, we rigorously…

We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…

A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…

Grazing set singularity leads to a surprising counter-example and breakdown of the classical mathematical theory for $L^{\infty}$ diffusive expansion of neutron transport equation with in-flow boundary condition in term of the Knudsen…

The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…

The article studies the transport equation that governes the motion of a fluid in a bounded domain, under the hypothesis of zero velocity at the boundary and supposing the incompressible nature of the fluid. Together with existence and…

This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…

In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using…

We study steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions and the source term decaying exponentially, we…