Two-Scale Convergence
نویسندگان
چکیده
منابع مشابه
Two-Scale Convergence
2 Two-Scale Convergence Definition and Results 15 2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Link with Weak Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Injection Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Two-Scale Convergence criterion . . . . . . . . . . . . . . . . . . ....
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Two-scale convergence is an important tool in homogenization theory. The contribution deals with its alternative definition based on two-scale mapping and transform. It removes the problems with choice of the space of admissible test functions and simplifies the proofs.
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Following an idea of G. Nguetseng, the author defines a notion of "two-scale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector-type theorem (i.e., which permits, in some cases, replacing a sequence by its "two-scale" limit, up to a st...
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متن کاملTwo - Scale Convergence . Some Remarks and Extensions
We first study the fundamental ideas behind two-scale convergence to enhance an intuitive understanding of this notion. The classical definitions and ideas are motivated with geometrical arguments illustrated by illuminating figures. Then a version of this concept, very weak two-scale convergence, is discussed both independently and briefly in the context of homogenization. The main features of...
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ژورنال
عنوان ژورنال: ESAIM: Proceedings
سال: 2012
ISSN: 1270-900X
DOI: 10.1051/proc/201238002