Related papers: Well posedness of fluid/solid mixture models for b…
In this work we propose a novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios. The model couples a system of kinetic transport equations…
Biofilm growth changes many physical properties of porous media such as porosity, permeability and mass transport parameters. The growth depends on various environmental conditions, and in particular, on flow rates. Modeling the evolution…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
Individual constituent balance equations are often used to derive expressions for species-specific segregation velocities in flows of dense granular mixtures. We propose a semiempirical expression for the interspecies momentum exchange in…
A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
This review article examines the complex dynamics of thin-film flows of granular suspensions spreading over rigid solid substrates with free air interfaces. Such systems feature an involved coupling of the free-surface dynamics with the…
The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady…
We consider the problem of waves propagating in a viscoelastic solid. For the material properties of the solid we consider both classical and fractional differentiation in time versions of the Zener, Maxwell, and Voigt models, where the…
We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…
We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…
Microfiltration technology is a widely used engineering strategy for fresh water production and water treatment. The major concern in many applications is the formation of a biological fouling layer leading to increased hydraulic resistance…
The phase-separation process of a binary mixture with order-parameter-dependent mobility under shear flow is numerically studied. The ordering is characterized by an alternate stretching and bursting of domains which produce oscillations in…
We consider the well-posedness of a model for a flow-structure interaction. This model describes the dynamics of an elastic flexible plate with clamped boundary conditions immersed in a supersonic flow. A perturbed wave equation describes…
Probing the fluid dynamics of thin films is an excellent tool to study the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid due to the fact that the dewetting process, an internal…
The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact…
The purpose of this paper is to deal with the issue of well-posedness for a class of non-Newtonian fluid dynamics equations. These sets of equations are commonly used to describe various complex models that appear in nature, industry, and…