Hermann Yonta Douanla

2019Article de revue

Deterministic Homogenization of Variational Inequalities with Unilateral Constraint

Project Euclid (Cornell University)

The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constraints. 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 and the convergence at infinity. Using the multiscale convergence method, we derive a homogenization result whose limit problem is of the same type as the problem with rapidly oscillating coefficients.

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2018PrépublicationAccès ouvert

Deterministic homogenization of variational inequalities with unilateral constraints

Hermann Douanla, Cyrille Kenne

arXiv (Cornell University)

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.

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2016PrépublicationAccès ouvert

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

Hermann Douanla, Erick Tetsadjio

arXiv (Cornell University)

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.

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2015PrépublicationAccès ouvert

Homogenization of reaction-diffusion equations in fractured porous media

Hermann Douanla, Jean Louis Woukeng

arXiv (Cornell University)

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.

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2012PrépublicationAccès ouvert

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

Hermann Douanla, Jean Louis Woukeng

arXiv (Cornell University)

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

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2012Article de revue

Homogenization of a nonlinear elliptic problem with large nonlinear potential

Hermann Douanla, Nils Svanstedt

Applicable Analysis

Homogenization is studied for a nonlinear elliptic boundary-value problem with a large nonlinear potential. More specifically we are interested in the asymptotic behaviour of a sequence of p-Laplacians of the form 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 ϵ of solutions converges weakly to u in W 1,p and the gradients D x u ϵ 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.

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2011PrépublicationAccès ouvert

Homogenization of Steklov spectral problems with indefinite density\n function in perforated domains

Hermann Douanla

arXiv (Cornell University)

The asymptotic behavior of second order self-adjoint elliptic Steklov\neigenvalue problems with periodic rapidly oscillating coefficients and with\nindefinite (sign-changing) density function is investigated in periodically\nperforated domains. We prove that the spectrum of this problem is discrete and\nconsists of two sequences, one tending to -{\\infty} and another to +{\\infty}.\nThe limiting behavior of positive and negative eigencouples depends crucially\non whether the average of the weight over the surface of the reference hole is\npositive, negative or equal to zero. By means of the two-scale convergence\nmethod, we investigate all three cases.\n

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2011Article de revue

Reiterated homogenization of linear eigenvalue problems in multiscale perforated domains beyond the periodic setting

Hermann Douanla, Nils Svanstedt

Chalmers Publication Library (Chalmers University of Technology)

Reiterated homogenization of linear elliptic Neuman eigenvalue problems in multiscale\nperforated domains is considered beyond the periodic setting. The classical\nperiodicity hypothesis on the coefficients of the operator is here substituted on each\nmicroscale by an abstract hypothesis covering a large set of concrete behaviors such\nas the periodicity, the almost periodicity, the weakly almost periodicity and many more\nbesides. Furthermore, the usual double periodicity is generalized by considering a type\nof structure where the perforations on each scale follow not only the periodic distribution\nbut also more complicated but realistic ones. Our main tool is Nguetseng’s Sigma\nconvergence.

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2010Article de revueAccès ouvert

Two-Scale Convergence of Stekloff Eigenvalue Problems in Perforated Domains

Hermann Douanla

Boundary Value Problems

By means of the two-scale convergence method, we investigate the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We prove a concise and precise homogenization result including convergence of gradients of eigenfunctions which improves the understanding of the asymptotic behavior of eigenfunctions. It is also justified that the natural local problem is not an eigenvalue problem.

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2013Article de revue

Two-scale convergence of periodic elliptic spectral problems with indefinite density function in perforated domains

Hermann Douanla

Asymptotic Analysis

Spectral asymptotics of linear periodic elliptic operators with indefinite (sign-changing) density function is investigated in perforated domains with the two-scale convergence method. The limiting behavior of positive and negative eigencouples depends crucially on whether the average of the weight over the solid part is positive, negative or equal to zero. We prove concise homogenization results in all three cases.

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2012PrépublicationAccès ouvert

Homogenization of a nonlinear elliptic problem with large nonlinear\n potential

Hermann Douanla, Nils Svanstedt

arXiv (Cornell University)

Homogenization is studied for a nonlinear elliptic boundary-value problem\nwith a large nonlinear potential. More specifically we are interested in the\nasymptotic behavior of a sequence of p-Laplacians of the form $$\n-\\text{div}(a(\\frac{x}{\\varepsilon})|Du_\\varepsilon|^{p-2}Du_\\varepsilon)\n+\\frac{1}{\\varepsilon}V(\\frac{x}{\\varepsilon})|u_\\varepsilon|^{p-2}u_\\varepsilon=f.\n$$ It is shown that, under a centring condition on the potential $V$, there\nexists a two-scale homogenized system with solution $(u, u_1)$ such that the\nsequence $u_\\varepsilon$ of solutions converges weakly to $u$ in $W^{1,p}$ and\nthe gradients $D_x u_\\varepsilon$ two-scale converges weakly to $D_x u+ D_y\nu_1$ in $L^p$, respectively. We characterize the limit system explicitly by\nmeans of two-scale convergence and a new convergence result.\n

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2011PrépublicationAccès ouvert

Two-scale convergence of elliptic spectral problems with indefinite density function in perforated domains

Hermann Douanla

arXiv (Cornell University)

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Hermann Yonta Douanla

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Publications

2019

Deterministic Homogenization of Variational Inequalities with Unilateral Constraint

2018

Deterministic homogenization of variational inequalities with unilateral constraints

2016

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

2015

Homogenization of reaction-diffusion equations in fractured porous media

2013

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

Incompressible viscous Newtonian flow in a fissured medium of general deterministic type

2012

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

Homogenization of a nonlinear elliptic problem with large nonlinear potential

2011

Homogenization of Steklov spectral problems with indefinite density\n function in perforated domains

Reiterated homogenization of linear eigenvalue problems in multiscale perforated domains beyond the periodic setting

2010

Two-Scale Convergence of Stekloff Eigenvalue Problems in Perforated Domains

Two-scale convergence of periodic elliptic spectral problems with indefinite density function in perforated domains

Homogenization of a nonlinear elliptic problem with large nonlinear\n potential

Homogenization of Steklov Spectral Problems with Indefinite Density Function in Perforated Domains

Two-scale convergence of elliptic spectral problems with indefinite density function in perforated domains

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