arXiv subjects

Hermann Douanla

Publications and source records attributed to Hermann Douanla.

5 recordsLinked to original sources

arXiv2018

Deterministic homogenization of variational inequalities with unilateral constraints

The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each scale a large set of concrete deterministic behavior such as the periodic, the almost periodic, the convergence at infinity. Using the multi-scale convergence method, we derive a homogenization result whose limit problem is of the same type as the problem with rapidly oscillating coefficients.

math-ph↗

arXiv2017

Reiterated homogenization of hyperbolic-parabolic equations in domains with tiny holes

This article studies the homogenization of hyperbolic-parabolic equations in porous media with tiny holes. We assume that the holes are periodically distributed and that the coefficients of the equations are periodic. Using the multi-scale convergence method, we derive a homogenization result whose limit problem is defined on a fixed domain and is of the same type as the problem with oscillating coefficients.

math.AP↗

arXiv2015

Homogenization of reaction-diffusion equations in fractured porous media

The paper deals with the homogenization of reaction-diffusion equations with large reaction terms in a multi-scale porous medium. We assume that the fractures and pores are equidistributed and that the coefficients of the equations are periodic. Using the multi-scale convergence method, we derive a homogenization result whose limit problem is defined on a fixed domain and is of convection-diffusion-reaction type.

math.AP↗

arXiv2012

Almost periodic homogenization of a generalized Ladyzhenskaya model for incompressible viscous flow

The paper deals with the existence and almost periodic homogenization of some model of generalized Navier-Stokes equations. We first establish an existence result for non-stationary Ladyzhenskaya equations with a given non constant density. The external force depends nonlinearly on the velocity. Next, to proceed with homogenization, as the density of the fluid is non constant, we combine the sigma-convergence method with some compactness arguments.

math.AP↗

arXiv2012

Homogenization of a nonlinear elliptic problem with large nonlinear potential

Homogenization is studied for a nonlinear elliptic boundary-value problem with a large nonlinear potential. More specifically we are interested in the asymptotic behavior of a sequence of p-Laplacians of the form $$ -\text{div}(a(\frac{x}{\varepsilon})|Du_\varepsilon|^{p-2}Du_\varepsilon) +\frac{1}{\varepsilon}V(\frac{x}{\varepsilon})|u_\varepsilon|^{p-2}u_\varepsilon=f. $$ It is shown that, under a centring condition on the potential $V$, there exists a two-scale homogenized system with solution $(u, u_1)$ such that the sequence $u_\varepsilon$ of solutions converges weakly to $u$ in $W^{1,p}$ and the gradients $D_x u_\varepsilon$ two-scale converges weakly to $D_x u+ D_y u_1$ in $L^p$, respectively. We characterize the limit system explicitly by means of two-scale convergence and a new convergence result.

math.AP↗