Related papers: Homogenization for advection-diffusion in a perfor…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
The sliced-Wasserstein flow is an evolution equation where a probability density evolves in time, advected by a velocity field computed as the average among directions in the unit sphere of the optimal transport displacements from its 1D…
We study the (generalized) one-dimensional population model developed by Anguige \& Schmeiser [1], which reflects cell-cell adhesion and volume filling under no-flux boundary condition. In this generalized model, depending on the adhesion…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
The steady motion of a viscous incompressible fluid in a multiply-connected, planar, bounded domain (perforated with a large number of small holes) is modeled through the Navier-Stokes equations with non-homogeneous Dirichlet boundary data…
One-dimensional free boundary problem for a nonlinear diffusion - convection equation with a Dirichlet condition at fixed face $x=0$, variable in time, is considered. Throught several transformations the problem is reduced to a free…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
We consider the one-dimensional Burgers equation randomly stirred at large scales by a Gaussian short-time correlated force. Using the method of dissipative anomalies, we obtain velocity and velocity-difference probability density functions…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
The advection-diffusion equation can be approximated by a one-dimensional diffusion equation in Lagrangian coordinates along the directions of compression of fluid elements (the stable manifold). This result holds in any number of…
Consider billiard dynamics in a strictly convex domain, and consider a trajectory that begins with the velocity vector making a small positive angle with the boundary. Lazutkin proved that in two dimensions, it is impossible for this angle…
This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on…
Two-scale homogenization limits of parabolic cross-diffusion systems in a heterogeneous medium with no-flux boundary conditions are proved. The heterogeneity of the medium is reflected in the diffusion coefficients or by the perforated…
A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at…
The decay of Burgers turbulence with compactly supported Gaussian "white noise" initial conditions is studied in the limit of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and…
This paper provides the first study of the homogenization of the 3D non-homogeneous incompressible Navier--Stokes system in perforated domains with holes of supercritical size. The diameter of the holes is of order $\varepsilon^{\alpha} \…
We consider the evolutionary compressible Navier-Stokes equations in a two-dimensional perforated domain, and show that in the subcritical case of very tiny holes, the density and velocity converge to a solution of the evolutionary…
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initial data, modelling simple shears and wall boundary layers,…
We investigate the non-perturbative results of multi-dimensional forced Burgers equation coupled to the continuity equation. In the inviscid limit, we derive the exact exponents of two-point density correlation functions in the universal…
In our recent work [8], we have studied the homogenization of the Poisson equation in a class of non periodically perforated domains. In this paper, we examine the case of the Stokes system. We consider a porous medium in which the…