Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit

Kévin Santugini

Displaying similar documents to “Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit”

Some properties of two-scale convergence

Augusto Visintin (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We reformulate and extend G. Nguetseng’s notion of two-scale convergence by means of a variable transformation, and outline some of its properties. We approximate two-scale derivatives, and extend this convergence to spaces of differentiable functions. The two-scale limit of derivatives of bounded sequences in the Sobolev spaces $W^{1, p} (R^{N})$ , $L_{r o t}^{2} {(R^{3})}^{3}$ , $L_{d i v}^{2} {(R^{3})}^{3}$ and $W^{2, p} (R^{N})$ is then characterized. The two-scale limit behaviour of the potentials of a two-scale convergent sequence of irrotational fields is finally studied. ...

Alternative approaches to the two-scale convergence

Luděk Nechvátal (2004)

Applications of Mathematics

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Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definition by Nguetseng and Allaire two alternative definitions are introduced and compared. They enable us to weaken requirements on the admissibility of test functions $ψ (x, y)$ . Properties and examples are added.

Mathematical theory of musical scales.

M. J. Garmendia Rodríguez, J. A. Navarro González (1996)

Extracta Mathematicae

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Our aim is to look for precise definitions of musical concepts. In this work we present the concepts we have been able to derive from the concept of pitch (high-low aspect of musical sounds). Now, pitches being the primitive concept, they will not be defined from a previous concept, but from their mutual relationships.

Homogenization of monotone parabolic problems with several temporal scales

Jens Persson (2012)

Applications of Mathematics

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In this paper we homogenize monotone parabolic problems with two spatial scales and any number of temporal scales. Under the assumption that the spatial and temporal scales are well-separated in the sense explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the “slow” self-similar case), rapid temporal oscillations, and rapid resonant...

Necessary conditions for a class of optimal control problems on time scales.

Zhan, Zaidong, Wei, W. (2009)

Abstract and Applied Analysis

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Homogenization of parabolic equations an alternative approach and some corrector-type results

Anders Holmbom (1997)

Applications of Mathematics

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We extend and complete some quite recent results by Nguetseng [Ngu1] and Allaire [All3] concerning two-scale convergence. In particular, a compactness result for a certain class of parameterdependent functions is proved and applied to perform an alternative homogenization procedure for linear parabolic equations with coefficients oscillating in both their space and time variables. For different speeds of oscillation in the time variable, this results in three cases. Further, we prove...