Related papers: Comparison principles and long time behavior for a…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
For a long-term forecast of the average air temperature in a metro tunnel and surrounding soil, heat balance conditions are modeled in a system that includes two parallel tunnels, a near-tunnels underground space, the earth's surface and…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…
Like any fluid heated from below, the atmosphere is subject to vertical instability which triggers convection. Convection occurs on small time and space scales, which makes it a challenging feature to include in climate models. Usually…
The competing influence of two types of interactions on surface diffusion is investigated: one of them, epsilon, acts between adsorbed particles, while the other one, eta, between activated and adsorbed particles. To this end, a specific…
In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary…
It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…
The aim of this paper is to apply the modified potential well method and some new differential inequalities to study the asymptotic behavior of solutions to the initial homogeneous $\hbox{Neumann}$ problem of a nonlinear diffusion equation…
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…
One-dimensional (vertical) models of planetary atmospheres typically balance the net solar and internal energy fluxes against the net thermal radiative and convective heat fluxes to determine an equilibrium thermal structure. Thus,simple…
We analyse the dynamics of a two dimensional system of interacting active dumbbells. We characterise the mean-square displacement, linear response function and deviation from the equilibrium fluctuation-dissipation theorem as a function of…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
We derive a uniqueness and stability principle for surface diffusion before the onset of singularities. The perturbations, however, are allowed to undergo topological changes. The main ingredient is a relative energy inequality, which in…
We provide a simple mathematical description of the exchange of energy between two fluids in an expanding Friedmann universe with zero spatial curvature. The evolution can be reduced to a single non-linear differential equation which we…
We study a system of diffusing-aggregating particles with deposition and evaporation of monomers. By combining theoretical and numerical methods, we establish a clearer understanding of the non-equilibrium phase transition known to occur in…
We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time…
A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation,…
We discuss the energy density,temperature and entropy of dark matter (DM) and dark energy (DE) as functions of the scale factor $a$ in an expanding universe. In a model of non-interacting dark components we repeat a derivation from…
We consider a Keller-Segel model with non-linear porous medium type diffusion and nonlocal attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen…