Feppon, Florian

We derive high order homogenized models for the incompressible Stokes system in a cubic domain filled with periodic obstacles. These models have the potential to unify the three classical limit problems (namely the ``unchanged' Stokes system, the Brinkman model, and the Darcy's law) corresponding to various asymptotic regimes of the ratio $\eta\equ...

Feppon, Florian Jing, Wenjia

This article is a sequel to our previous work [13] concerned with the derivation of high-order homogenized models for the Stokes equation in a periodic porous medium. We provide an improved asymptotic analysis of the coefficients of the higher order models in the low-volume fraction regime whereby the periodic obstacles are rescaled by a factor $\e...

Beale, J. Thomas Nishida, Takaaki Teramoto, Yoshiaki

"Regularity and Asymptotic Analysis for Critical Cases of Partial Differential Equations". May 29-31, 2019. edited by Takayoshi Ogawa, Keiichi Kato, Mishio Kawashita and Masashi Misawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / We consider the Stokes system arising in free surface viscous flows...

Sun, Chenmin

We study the quasi-mode of the Stokes system posed on a smooth bounded domain X with Dirichlet boundary condition. We prove that the semi-classical defect measure associated with a sequence of solutions concentrates on the bicharacteristics of Laplacian as a matrix-valued Radon measure. Moreover, we show that the support of the measure is invariant...

Asier Bárcena-Petisco, Jon

In this paper we consider a Stokes system with Navier-slip boundary conditions. The main results concern the behaviour of the cost of null controllability with respect to the diffusion coefficient when the control acts in the interior. In particular, we prove in the square that for a sufficiently large time the cost decays exponentially as the diff...

khayat, faten

In this work, we prove the quadratic convergence of the Levenberg-Marquardt method for the inverse problem of identifying a Robin coefficient for the Stokes system, where we suppose that this parameter is piecewise constant on some non accessible part of the boundary and under the assumption that on this part, the velocity of a given reference solu...

Haslinger, Jaroslav Kučera, Radek Šátek, Václav

The theoretical part of the paper analyzes discretized Stokes systems with local Coulomb's slip boundary conditions. Solutions to discrete models are defined by means of fixed-points of an appropriate mapping. We prove the existence of a fixed-point, establish conditions guaranteeing its uniqueness and examine how they depend on the discretization ...

Ruas, Vitoriano

Among a few known techniques the isoparametric version of the finite element method for meshes consisting of curved triangles or tetrahedra is the one most widely employed to solve PDEs with essential conditions prescribed on curved boundaries. It allows to recover optimal approximation properties that hold for elements of order greater than one in...

Anguiano, María Suárez-Grau, Francisco J.

We consider the Stokes system in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size ε. On the boundary of the cylinders we prescribe non-homogeneous slip boundary conditions depending on a parameter γ. The aim is to give the asymptotic behavior of the velocity and the pressure of the fluid...

Sun, Chenmin

In this thesis, we deal with the control and stabilization for certain hyperbolic and dispersive partial differential equations. The first part of this work is devoted to the stabilization of hyperbolic Stokes equation. The propagation of singularity for semi-classical Stokes system is established in Chapter 1. This will be done by adpating the str...