相关论文: Coupled transport equations with freezing
We consider the junction of multiple one-dimensional systems and study how conserved currents transport at the junction. To characterize the transport process, we introduce reflection/transmission coefficients by applying boundary conformal…
This paper gives a concise but rigorous mathematical description of a material control volume that is separated into two parts by a singular surface at which physical states are discontinuous. The geometrical background material is…
Following the analytic approach to thermodynamics developed by Stueckelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations…
A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial…
We obtain a sharp limit H\"older continuity of the solution for the transport equations thanks to a vanishing viscosity analysis. We also derive the same control for parabolic equations and for inviscid Burgers' equation. Eventually, under…
We set up and study a coupled problem on stationary non-isothermal flow of electrorheological fluids. The problem consist in finding functions of velocity, pressure and temperature which satisfy the motion equations, the condition of…
We analyze the functional equation $$F(x+F(x))=-F(x)$$ and reveal its relationship with a system of partial differential equations arising as the hydrodynamic limit of a system of pinned billiard balls on the line. The system of balls must…
Transportation Problem is an important problem which has been widely studied in Operations Research domain. It has been often used to simulate different real life problems. In particular, application of this Problem in NP Hard Problems has…
The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…
We consider the stochastic transport equation with a possibly unbounded H\"older continuous vector field. Well-posedness is proved, namely, we show existence, uniqueness and strong stability of W^{1,p}-weak solutions.
This article is concerned with the study of weak solutions of a linear transport equation on a bounded domain with coupled boundary data for general non smooth space and time dependent velocity fields. The existence of solutions, its…
We study coupled transport in the nonequilibrium stationary state of a model consisting of independent random walkers, moving along a one-dimensional channel, which carry a conserved energy-like quantity, with density and temperature…
We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist…
In this paper we analyze a coupled system between a transport equation and an ordinary differential equation with time delay (which is a simplified version of a model for kidney blood flow control). Through a careful spectral analysis we…
We prove some existence, uniqueness and non-existence results of stochastic strong solutions for a class of stochastic transport equations with a $q$-integrable (in time), bounded and $\alpha$-H\"{o}lder continuous (in space) drift…
Transport through two one-dimensional interacting metals (Luttinger liquids) coupled together at a single point is analyzed. The dominant coupling mechanism is shown to be of electrostatic nature. Describing the voltage sources by boundary…
In this work, we demonstrate well-posedness and regularisation by noise results for a class of geometric transport equations that contains, among others, the linear transport and continuity equations. This class is known as linear advection…
Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space-time symmetries of the corresponding equations of motion. A systematic analysis of…
Ultracold atoms confined by engineered magnetic or optical potentials are ideal systems for studying phenomena otherwise difficult to realize or probe in the solid state because their atomic interaction strength, number of species, density,…
We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows to deduce a scalar Generalized Porous Medium Equation for…