Related papers: Quasistatic Droplet percolation
The method of matched asymptotic expansions is used to study the canonical problem of steady laminar flow through a narrow two-dimensional channel blocked by a tight-fitting finite-length highly permeable porous obstacle. We investigate the…
We investigate quantitative properties of nonnegative solutions $u(t,x)\ge 0$ to the nonlinear fractional diffusion equation, $\partial_t u + \mathcal{L}F(u)=0$ posed in a bounded domain, $x\in\Omega\subset \mathbb{R}^N$, with appropriate…
We perform a linear stability analysis of three-layer radial porous media and Hele-Shaw flows with variable viscosity in the middle layer. A nonlinear change of variables results in an eigenvalue problem that has time-dependent coefficients…
We study the long-time behavior of solutions of the one-phase Stefan problem in inhomogeneous media in dimensions $n \geq 2$. Using the technique of rescaling which is consistent with the evolution of the free boundary, we are able to show…
We study the homogenization of the Dirichlet problem for the Stokes equations in $\mathbb{R}^3$ perforated by $m$ spherical particles. We assume the positions and velocities of the particles to be identically and independently distributed…
The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in…
This paper rediscovers a classical homogenization result for a prototypical linear elliptic boundary value problem with periodically oscillating diffusion coefficient. Unlike classical analytical approaches such as asymptotic analysis,…
This paper proposes a new approach to solving the Buckley-Leverett System, which is to consider a compressible approximation model characterized by a stiff pressure law. Passing to the incompressible limit, the compressible model gives rise…
In this paper we prove convergence results for the homogenization of the Dirichlet problem with rapidly oscillating boundary data in convex polygonal domains. Our analysis is based on integral representation of solutions. Under a certain…
We consider the homogenization of a semilinear heat equation with vanishing viscosity and with oscillating positive potential depending on $u/\varepsilon$. According to the rate between the frequency of oscillations in the potential and the…
In this paper, we present a nonlocal model for Poisson equation and corresponding eigenproblem with Dirichlet boundary condition. In the direct derivation of the nonlocal model, normal derivative is required which is not known for Dirichlet…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in…
We rigorously prove the convergence of appropriately scaled solutions of the 2D Hele-Shaw moving boundary problem with surface tension in the limit of thin threads to the solution of the formally corresponding Thin Film equation. The proof…
This work analyses the homogenization of a linear elliptic equation with Neumann boundary conditions in a comb/brush domain, composed of a fixed base and a family of thin teeth. The teeth are defined as rescalings of order less than or…
We consider the following fractional semilinear Neumann problem on a smooth bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, $$\begin{cases} (-\varepsilon\Delta)^{1/2}u+u=u^{p},&\hbox{in}~\Omega,\\ \partial_\nu…
We consider the homogenization of parabolic equations with large spatially-dependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We…
In this article we investigate averaging properties of fully nonlinear PDEs in bounded domains with oscillatory Neumann boundary data. The oscillation is periodic and is present both in the operator and in the Neumann data. Our main result…
A Bernoulli free boundary problem with geometrical constraints is studied. The domain $\Om$ is constrained to lie in the half space determined by $x_1\geq 0$ and its boundary to contain a segment of the hyperplane $\{x_1=0\}$ where…