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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…
A hybrid numerical model previously developed for combustion simulations is extended in this article to describe flame propagation and stabilization in porous media. The model, with a special focus on flame/wall interaction processes, is…
Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
We propose a Langevin equation for systems in an environment with nonuniform temperature. At odds with an older proposal, ours admits a locally Maxwellian steady state, local equipartition holds and for detailed-balanced (reversible)…
Due to spatial scarcity and uncertainties in sediment data, initial and boundary conditions in deep-time climate simulations are not well constrained. On the other hand, the climate is a nonlinear system with a multitude of feedback…
We introduce an elementary model of a turbulent boundary layer over a flat surface, given as a vertical random distribution of spanwise Lamb-Oseen vortex configurations placed over a non-slip boundary condition line. We are able to…
In this work, we consider not only a discontinuous boundary-value problem with retarded argument and four supplementary transmission conditions at the two points of discontinuities but also, eigenparameter-dependent boundary conditions and…
A compressible laminar boundary layer developing over an isotropic porous substrate is investigated by asymptotic and numerical methods. The substrate is modeled as an array of cubes. The momentum and enthalpy balance equations are derived…
We study the well-posedness of the compressible boundary layer equations with data being analytic in the tangential variable of the boundary. The compressible boundary layer equations, a nonlinear coupled system of degenerate parabolic…
The mechanisms governing the transition to turbulence in natural convection boundary layers along strongly heated vertical walls remain neither very clear nor well understood, because of the lack of experiments and the difficulties of…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the…
An algorithm is proposed to implement unsteady jump boundary conditions, presenting discontinuity in physical quantities, within the lattice Boltzmann method (LBM). This is useful to tackle problems involving mass or heat transfer through…
The equation for temporary evolution of spectral energy of collisionless Alfven waves is derived in framework of weak turbulence theory. The main nonlinear processes for such conditions are induced scattering and two quantum absorption of…
The turbulence statistics of the intermittent region in a supersonic turbulent boundary layer are studied by direct numerical simulation. Recently, Kwon et al. (2016) have shown that this intermittent behavior, consisting of the coexistence…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions…
Convection-diffusion of heat transfer is one of the important phenomena in fluid flow and industrial problems. The involved parameters, boundary conditions, and material properties are greatly affecting the same. As such, the uncertainness…
The paper is denoted to the initial-boundary value problem for the wave equation with the Sturm-Liouville operator with irregular (distributive) potentials. To obtain a solution to the equation, the separation method and asymptotics of the…