Alternative approaches to the two-scale convergence

Luděk Nechvátal

Displaying similar documents to “Alternative approaches to the two-scale convergence”

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. ...

Some remarks on two-scale convergence and periodic unfolding

Jan Franců, Nils E M Svanstedt (2012)

Applications of Mathematics

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The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives...

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...