Generalized Darcy–Oseen resolvent problem

In this paper we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system we consider two auxiliary problem: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations

Integral representation of a solution to the Stokes-Darcy problem

With methods of potential theory we develop a representation of a solution of the coupled Stokes-Darcy model in a Lipschitz domain for boundary data in H-1/2

Approximate Approximations for the Poisson and the Stokes Equations

Abstract The method of approximate approximations is based on generating functions representing an approximate partition of the unity, only. In the present paper this method is used for the numerical solution of the Poisson equation and the Stokes system in R n (n = 2, 3). The corresponding approximate volume potentials will be computed explicitly in these cases, containing a one-dimensional integral, only. Numerical simulations show the efficiency of the method and confirm the expected convergence of essentially second order, depending on the smoothness of the data. Mathematics Subject Classifications: 31B10, 35J05, 41A30, 65N12, 76D0

Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces

INTEGRANTES EQUIPO DE EDUCACIÓN VIAL EN MADRID [Material gráfico]

Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201

The equations of non-homogeneous asymmetric

We study the existence and uniqueness of strong solutions for the equations of non-homogeneous asymmetric uids. We use an iterative approach and we prove that the approximate solutions constructed by this method converge to the strong solution of these equations. We also give bounds for the rate of convergence

On the mixed problem for the semilinear Darcy-Forchheimer-Brinkman PDE system in Besov spaces on creased Lipschitz domains

The purpose of this paper is to study the mixed Dirichlet-Neumann boundary value problem for the semilinear Darcy- Forchheimer-Brinkman system in Lp-based Besov spaces on a bounded Lipschitz domain in R3, with p in a neighbourhood of 2. This system is obtained by adding the semilinear term juju to the linear Brinkman equation. First, we provide some results about equivalence between the Gagliardo and non-tangential traces, as well as between the weak canonical conormal derivatives and the non-tangential conormal derivatives. Various mapping and invertibility properties of some integral operators of potential theory for the linear Brinkman system, and well posedness results for the Dirichlet and Neumann problems in Lp-based Besov spaces on bounded Lipschitz domains in Rn (n 3) are also presented. Then, employing integral potential operators, we show the well-posedness in L2-based Sobolev spaces for the mixed problem of Dirichlet-Neumann type for the linear Brinkman system on a bounded Lipschitz domain in Rn (n 3). Further, by using some stability results of Fredholm and invertibility properties and exploring invertibility of the associated Neumann-to-Dirichlet operator, we extend the well-posedness property to some Lp-based Sobolev spaces. Next we use the well-posedness result in the linear case combined with a xed point theorem in order to show the existence and uniqueness for a mixed boundary value problem of Dirichlet and Neumann type for the semilinear Darcy-Forchheimer-Brinkman system in Lp-based Besov spaces, with p 2 (2 "; 2 + ") and some parameter " > 0

Finite differences and boundary element methods for non-stationary viscous incompressible flow

We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is carried out