Related papers: Finite Volumes for a dissipative free boundary pro…
We consider a flow of non-Newtonian heat conducting incompressible fluid in a bounded domain subjected to the homogeneous Dirichlet boundary condition for the velocity field and the spatially inhomogeneous Dirichlet boundary condition for…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discretisations of such models, in which internal fluxes are not…
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…
We consider a nonlinear, free boundary fluid-structure interaction model in a bounded domain. The viscous incompressible fluid interacts with a nonlinear elastic body on the common boundary via the velocity and stress matching conditions.…
In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 < $\alpha$ < 1. We turn the free interface problem…
The celebrated experiment of Tuval et al. \cite{tuval2005bacterial} showed that the bacteria living a water drop can form a thin layer near the air-water interface, where a so-called chemotaxis-fluid system with physical boundary conditions…
We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…
In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK collision operator. Thanks to appropriate uniform estimates,…
This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential…
We study the free boundary regularity of the traveling wave solutions to a degenerate advection-diffusion problem of Porous Medium type, whose existence was proved in \cite{MonsaingonNovikovRoquejoffre}. We set up a finite difference scheme…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
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…
This paper is concerned with the global well-posedness of a chemotaxis-Euler system in bounded domains of $\mathbb{R}^2$. Completing the system with physical boundary conditions, we show that the corresponding initial boundary value problem…
A general analytic solution to the fractional advection diffusion equation is obtained in plane parallel geometry. The result is an infinite series of spatial Fourier modes which decay according to the Mittag-Leffler function, which is cast…
We investigate in this paper the global stability of the compressible viscous surface waves in the absence of surface tension effect with a steady-state violating Rayleigh-Taylor instability and the reference domain being the horizontal…
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…
The global existence and boundedness of solutions to volume-surface reaction diffusion systems with a mass control condition are investigated. Such systems arise typically in e.g. cell biology, ecology or fluid mechanics, when some…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…