相关论文: Boundary Layer of Transport Equation with In-Flow …
We introduce Wasserstein-like dynamical transport distances between vector-valued densities on the real line. The mobility function from the scalar theory is replaced by a mobility matrix, that is subject to positivity and concavity…
In most results concerning bounds on the heat transport in the Rayleigh-B\'{e}nard convection problem no-slip boundary conditions for the velocity field are assumed. Nevertheless it is debatable, whether these boundary conditions reflect…
The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross-section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures and they are assumed to be impermeable.…
Using the advection-diffusion equation, we analytically study contaminant transport in a sharply contrasting medium with a diffusion barrier due to localization of a contaminant source in a low-permeability medium. Anomalous diffusion…
We propose a new mathematical model of groundwater flow in porous medium layered over inclined impermeable bed. In its full generality, this is a free-surface problem. To obtain analytically tractable model, we use generalized…
A rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation with the diffuse reflection boundary condition has been a challenging open problem. We settle this open…
We study a toy model for the evolution of the oxygen concentration in an oxide layer. It consists in a transient convection diffusion equation in a one-dimensional domain of variable width. The motions of the boundaries are governed by the…
A two-phase two-component model is formulated for the advective-diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free-boundary problem has a unique…
We study the nonhomogeneous boundary value problem for the Navier--Stokes equations of steady motion of a viscous incompressible fluid in a three--dimensional exterior domain with multiply connected boundary. We prove that this problem has…
We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for…
We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
We consider the local kinematics at fluid interfaces in two-phase flows within the sharp interface framework. In the considered case with phase change and slip at the interface, the governing velocity field is discontinuous at the phase…
A mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the continuity equations, which reflect the well-known physical…
This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, Matsumura and Nishihara showed in [A. Matsumura and K. Nishihara, Large-time behaviors of solutions to an…
Atmospheric convection is an essential aspect of atmospheric movement, and it is a source of errors in Climate Models. Being able to generate approximate limit formulas and compare the estimations they produce, could give a way to reduce…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
A one-dimensional cross-diffusion system modeling the transport of vesicles in neurites is analyzed. The equations are coupled via nonlinear Robin boundary conditions to ordinary differential equations for the number of vesicles in the…
Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed, either for classes of theories or (by using general arguments) universally for all theories.…
Motivated by lubrication problems, we consider a micropolar uid ow in a 2D domain with a rough and free boundary. We assume that the thickness and the roughness are both of order 0 < " << 1. We prove the existence and uniqueness of a…