Related papers: Porous medium equation to Hele-Shaw flow with gene…
A phase transition model for porous media in consolidation is studied. The model is able to describe the phenomenon of fluid-segregation during the consolidation process, i.e., the coexistence of two phases differing from fluid content…
When a viscous fluid partially fills a Hele--Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman--Taylor instability. We consider the evolution of a fluid region of finite extent, bounded…
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy's law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions…
We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling…
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 show existence and uniqueness of very weak solutions of the Cauchy problem for the porous medium equation on Cartan-Hadamard manifolds satisfying suitable lower bounds on Ricci curvature, with initial data that can grow at infinity at a…
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 work, we introduce a cross-diffusion model that couples population density and occupied area to investigate how internal pressure drives growth and motility. By blending nonlinear nonlocal interactions with porous-medium diffusion…
We study the linear stability of the displacement of three Stokes fluids with constant viscosity in a porous medium when the middle fluid is contained in a bounded region. We use the Hele-Shaw model. The eigenfunctions of the stability…
We study a nonlinear porous medium type equation involving the infinity Laplacian operator. We first consider the problem posed on a bounded domain and prove existence of maximal nonnegative viscosity solutions. Uniqueness is obtained for…
We consider the process of convective dissolution in homogeneous and isotropic porous media. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is…
We consider a diffuse interface model for tumor growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation, which models a tumor growing in the presence of a nutrient species and surrounded by…
We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the non-local character of the interface dynamics, due to liquid…
We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…
A circular Hele-Shaw cell bounded by a volumetrically confined elastic solid can act as a fluidic fuse: during radially outward fluid flow, the solid deforms in response to the viscous pressure field such that the gap expands near the inlet…
We revisit the problem of proving the incompressible limit for the compressible porous media equation with Newtonian drift and growth. The question is motivated by models of living tissues development including chemotaxis. We extend the…
We study the Cahn-Hilliard-Biot model with respect to its mathematical well-posedness. The system models flow through deformable porous media in which the solid material has two phases with distinct material properties. The two phases of…
We study a porous medium equation with fractional potential pressure: $$ \partial_t u= \nabla \cdot (u^{m-1} \nabla p), \quad p=(-\Delta)^{-s}u, $$ for $m>1$, $0<s<1$ and $u(x,t)\ge 0$. To be specific, the problem is posed for $x\in…
We study a diffuse interface model describing the evolution of the flow of a binary fluid in a Hele-Shaw cell. The model consists of a Cahn-Hilliard-Darcy (CHD) type system with transport and mass source. A relevant physical application is…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…