Periodic solutions for an evaporation problem with a Signorini type boundary condition
Peristaltic transport in a cylindrical tube through a porous medium.
Problèmes à frontière libre en hydraulique : milieux non homogènes
Problèmes unilatéraux pour des équations non linéaires de convection-réaction
Processi di filtrazione in un mezzo poroso con interazioni fra il liquido e la matrice porosa
A model of filtration in a multispecies porous medium accompanied by a strong interaction between the flow and the porous matrix is presented. The species removed by the flow are both fine particles and other substances which diffuse in the liquid. The accumulation of the migrating particles in proximity of the outflow surface gives rise to the formation of a compact layer with high hydraulic resistance. The corresponding mathematical model consists in a set of partial differential equations of...
Productivity formulas for a partially penetrating vertical well in a circular cylinder drainage volume.
Propagation of seismic waves in block elastic-fluid media. III.
Pseudo-steady-state productivity formula for a partially penetrating vertical well in a box-shaped reservoir.
Pulsatile flow of couple stress fluid through a porous medium with periodic body acceleration and magnetic field.
Qualitative investigation of nonlinear differential equations describing infiltration of water
A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.
Radiative mixed convection over an isothermal cone embedded in a porous medium with variable permeability.
Radiaton effects on unsteady MHD free convection with Hall current near an infinite vertical porous plate.
Reactive transport through an array of cells with semi-permeable membranes
Regularity of solutions of the fractional porous medium flow
We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. The precise model is . The problem is posed in with nonnegative initial data that are integrable and decay at infinity. A previous paper has established the existence of mass-preserving, nonnegative weak solutions satisfying energy estimates and finite propagation. As main results we establish the boundedness and regularity of such weak solutions. Finally, we extend the existence...
Regularization and stabilization of discrete saddle-point variational problems.
Relaxation of the incompressible porous media equation
It was shown recently by Córdoba, Faraco and Gancedo in [1] that the 2D porous media equation admits weak solutions with compact support in time. The proof, based on the convex integration framework developed for the incompressible Euler equations in [4], uses ideas from the theory of laminates, in particular configurations. In this note we calculate the explicit relaxation of IPM, thus avoiding configurations. We then use this to construct weak solutions to the unstable interface problem (the...
Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...
Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...
Revisited isoperimetric inequalities for the p-capacity and application to the muskat problem
Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media
Asymptotic error expansions in the sense of -norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing...