Existence and uniqueness of periodic solutions for a model of contaminant flow in porous medium.
Existence and uniqueness of solutions for a degenerate quasilinear parabolic problem.
We consider the following quasilinear parabolic equation of degenerate type with convection term ut = φ (u)xx + b(u)x in (-L,0) x (0,T). We solve the associate initial-boundary data problem, with nonlinear flux conditions. This problem describes the evaporation of an incompressible fluid from a homogeneous porous media. The nonlinear condition in x = 0 means that the flow of fluid leaving the porous media depends on variable meteorological conditions and in a nonlinear manner on u. In x = -L we...
Existence de solutions faibles pour un modèle d'écoulement triphasique en milieu poreux
Existence of solutions for a degenerate seawater intrusion problem.
Existence of solutions of a nonlinear system modelling fluid flow in porous media.
Extension of a regularity result concerning the dam problem
One proves, in the case of piecewise smooth coefficients, that the time derivative of the solution of the so called dam problem is a measure, extending the result proved by the same authors in the case of Lipschitz continuous coefficients.
Extinction and decay estimates of solutions for a class of porous medium equations.
Finite bandwidth, long wavelength convection with boundary imperfections: Near-resonant wavelength excitation.
Finite element discretization of Darcy's equations with pressure dependent porosity
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose...
Finite element in modeling of flow in porous media: How to describe wells.
Finite speed of propagation for a non-local porous medium equation
This note is concerned with proving the finite speed of propagation for some non-local porous medium equation by adapting arguments developed by Caffarelli and Vázquez (2010).
Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities
We study a one-dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated nonlinear parabolic equations spatially coupled by nonlinear transmission conditions. We approximate the solution of our problem thanks to a monotonous finite volume scheme. The convergence of the underlying discrete solution to a weak solution when the discretization step...
Fluid flow in macromolecular systems and related perturbation problems
Free boundary eigenfunctions for a nonlinear degenerate eigenvalue problem.
Free convective flow of a stratified fluid through a porous medium bounded by a vertical plane.
Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.
We establish the uniqueness of fundamental solutions to the p-Laplacian equationut = div (|Du|p-2 Du), p > 2,defined for x ∈ RN, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equationut = ∆(um), m > 1,giving new and simpler proofs of known results. We finally introduce yet another method of proving asymptotic results based on the...
Geothermal flow in porous media
Global BV solutions for a model of multi-species mixture in porous media
Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media
We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing...
Groundwater pollutant transport: transforming layered models to dynamical systems.