Reiterated Ergodic Algebras and Applications

Nguetseng, Gabriel; Sango, Mamadou; Woukeng, Jean Louis

doi:10.1007/s00220-010-1127-3

Cited by 46 publications

(61 citation statements)

References 18 publications

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“…Recently, using an idea introduced by Zhikov and Krivenko [45] in the framework of the theory of algebras with mean, and developed by CasadoDiaz and Gayte [9,10], Nguetseng et al [30] show a new way of looking at the algebras of homogenization, the so-called H-subalgebras on R d for H. But this extension does not destroy bases pre-established in [23]; that is why our work in the sequel based on the concept of H-algebras, follows ideas in both [23] and [30]. Assume that A is an H-algebra on R d z .…”

Section: Fundamentals Of Homogenizationmentioning

confidence: 99%

Deterministic homogenization of weakly damped nonlinear hyperbolic-parabolic equations

Nnang

2011

Nonlinear Differ. Equ. Appl.

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Abstract. Deterministic homogenization is studied for nonlinear hyperbolic-parabolic equations with a linear damping term. It is shown by the sigma-convergence method that the sequence of solutions to a class of highly oscillatory nonlinear evolution problems converges to the solution to a homogenized quasilinear hyperbolic-parabolic problem. Mathematics subject classification (1991). 35B40, 46J10.

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Section: Fundamentals Of Homogenizationmentioning

confidence: 99%

Deterministic homogenization of weakly damped nonlinear hyperbolic-parabolic equations

Nnang

2011

Nonlinear Differ. Equ. Appl.

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“…In that direction we refer, e.g., to the papers [15,30,32,33,34,54,58,59,56,31] in which only ergodic algebras are considered. In this paper we show how one can derive general homogenization results in algebras with mean value through the theory of strongly continuous groups of transformation.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Homogenization in algebras with mean value

Woukeng¹

2015

Banach J. Math. Anal.

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Abstract. In several works, the theory of strongly continuous groups is used to build a framework for solving stochastic homogenization problems. Following this idea, we construct a detailed and comprehensive theory of homogenization. This enables to solve homogenization problems in algebras with mean value, regardless of whether they are ergodic or not, thereby responding affirmatively to the question raised by Zhikov and Krivenko [V.V. Zhikov, E.V. Krivenko, Homogenization of singularly perturbed elliptic operators. Matem. Zametki, 33 (1983) 571-582 (english transl.: Math. Notes, 33 (1983) 294-300)] to know whether it is possible to homogenize problems in nonergodic algebras. We also state and prove a compactness result for Young measures in these algebras. As an important achievement we study the homogenization problem associated with a stochastic Ladyzhenskaya model for incompressible viscous flow, and we present and solve a few examples of homogenization problems related to nonergodic algebras.

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“…The interest of the two-scale convergence follows from the classical compactness results which establishes the existence of a two-scale limit for bounded sequences in L 2 (see [1,7,8,[14][15][16]). As a consequence of these results and…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, the compactness property of the two-scale convergence (see [1,7,8,[14][15][16]) implies the existence of…”

Section: Lemma 41 We Consider a Bounded Sequencementioning

confidence: 99%

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A corrector for a wave problem with periodic coefficients in a 1D bounded domain

et al. 2015

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Abstract. We consider a wave problem posed in a bounded open interval of R, where the coefficients, the initial conditions and the right-hand side are highly oscillating, periodic in the space variable and almost periodic in the time one. Our purpose is to find not only the corresponding limit equation but a corrector, i.e. a strong approximation in the H 1 topology, which for the wave equation is known to be non-local. In a previous paper we have studied this problem in the whole R N , here we consider the case of a bounded domain in dimension one. Thus the novelty in this paper is the analysis of the boundary conditions. Mathematics Subject Classification. 35B27, 35L20.

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Reiterated Ergodic Algebras and Applications

Cited by 46 publications

References 18 publications

Deterministic homogenization of weakly damped nonlinear hyperbolic-parabolic equations

Deterministic homogenization of weakly damped nonlinear hyperbolic-parabolic equations

Homogenization in algebras with mean value

A corrector for a wave problem with periodic coefficients in a 1D bounded domain

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