Displaying similar documents to “Multiscale stochastic homogenization of convection-diffusion equations”

Stochastic homogenization of a class of monotone eigenvalue problems

Nils Svanstedt (2010)

Applications of Mathematics

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Stochastic homogenization (with multiple fine scales) is studied for a class of nonlinear monotone eigenvalue problems. More specifically, we are interested in the asymptotic behaviour of a sequence of realizations of the form - div a T 1 x ε 1 ω 1 , T 2 x ε 2 ω 2 , ∇ u ε ω = λ ε ω 𝒞 ( u ε ω ) . It is shown, under certain structure assumptions on the random map a ( ω 1 , ω 2 , ξ ) , that the sequence { λ ε ω , k , u ε ω , k } of k th eigenpairs converges to the k th eigenpair { λ k , u k } of the homogenized eigenvalue problem - div ( b ( ∇ u ) ) = λ 𝒞 ¯ ( u ) . For the case of p -Laplacian type maps we characterize b explicitly.

Σ -convergence of nonlinear monotone operators in perforated domains with holes of small size

Jean Louis Woukeng (2009)

Applications of Mathematics

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This paper is devoted to the homogenization beyond the periodic setting, of nonlinear monotone operators in a domain in ℝ N with isolated holes of size ε 2 ( ε > 0 a small parameter). The order of the size of the holes is twice that of the oscillations of the coefficients of the operator, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The usual periodic perforation of the domain and the classical periodicity hypothesis on the coefficients...

Regularity of the effective diffusivity of random diffusion with respect to anisotropy coefficient

M. Cudna, T. Komorowski (2008)

Studia Mathematica

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We show that the effective diffusivity of a random diffusion with a drift is a continuous function of the drift coefficient. In fact, in the case of a homogeneous and isotropic random environment the function is C ∞ smooth outside the origin. We provide a one-dimensional example which shows that the diffusivity coefficient need not be differentiable at 0.

On some nonlocal systems containing a parabolic PDE and a first order ODE

Ádám Besenyei (2010)

Mathematica Bohemica

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Two models of reaction-diffusion are presented: a non-Fickian diffusion model described by a system of a parabolic PDE and a first order ODE, further, porosity-mineralogy changes in porous medium which is modelled by a system consisting of an ODE, a parabolic and an elliptic equation. Existence of weak solutions is shown by the Schauder fixed point theorem combined with the theory of monotone type operators.

Homogenization of periodic non self-adjoint problems with large drift and potential

Grégoire Allaire, Rafael Orive (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the homogenization of both the parabolic and eigenvalue problems for a singularly perturbed convection-diffusion equation in a periodic medium. All coefficients of the equation may vary both on the macroscopic scale and on the periodic microscopic scale. Denoting by the period, the potential or zero-order term is scaled as ε - 2 and the drift or first-order term is scaled as ε - 1 . Under a structural hypothesis on the first cell eigenvalue, which is assumed to admit a unique minimum...