Related papers: Modeling of a heat equation with a Dirac density
We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model…
We consider a system of partial differential equations describing the steady flow of a compressible heat conducting Newtonian fluid in a three-dimensional channel with inflow and outflow part. We show the existence of a strong solution…
We introduce the transportation-annihilation distance $W_p^\sharp$ between subprobabilities and derive contraction estimates with respect to this distance for the heat flow with homogeneous Dirichlet boundary conditions on an open set in a…
The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…
We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in…
We study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible Navier-Stokes-Fourier system. Our main result is the existence of a weak solution to these…
The non-equilibrium thermodynamics of relativistic systems have a rich phenomenology. The simplest phenomenon in the class of dissipative processes is that of heat. This letter presents a brief summary of the efforts made to tackle the…
We investigate a one-dimenisonal Hamiltonian system that describes a system of particles interacting through short-range repulsive potentials. Depending on the particle mean energy, $\epsilon$, the system demonstrates a spectrum of kinetic…
Based on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a…
The Dirac equation offers a precise analytical description of relativistic two-particle bound states, when one of the constituent is very heavy and radiative corrections are neglected. Looking at the high-Z hydrogen-like atom in the…
We present a numerical study of convection in a horizontal layer comprising a fluid-saturated porous bed overlain by an unconfined fluid layer. Convection is driven by a vertical, destabilising temperature difference applied across the…
In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb R_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a…
In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this…
Dense mixture of granules and liquid often shows a sever shear thickening and is called a dilatant fluid. We construct a fluid dynamics model for the dilatant fluid by introducing a phenomenological state variable for a local state of…
We consider convection in an internally heated layer of fluid that is bounded below by a perfect insulator and above by a poor conductor. The poorly conducting boundary is modelled by a fixed heat flux. Using solely analytical methods, we…
We study temperature distribution in a heat conducting problem, for a system of p-Laplace equation, giving rise to a free boundary.
Depletion of the liquid density near a solid surface with a weak long-range fluid-surface interaction was studied by computer simulations of the liquid-vapor coexistence of a LJ fluid confined in slitlike pores. In a wide temperature range…
In this paper we study thermo-electric transport in interacting two-dimensional Dirac-type systems using a phenomenological Boltzmann approach. We consider a setup that can accommodate electrons, holes, and collective modes. In the first…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a contact line. This is a main challenge in numerical simulations of two-phase flows with moving contact lines. We derive a two-dimensional…
We rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed by Garcke et al. to weak (varifold) solutions of the corresponding sharp-interface problem for a…