The General Theory of Homogenization A Personalized Introduction /
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various...
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| Format: | Electronic |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
2010.
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| Series: | Lecture Notes of the Unione Matematica Italiana,
7 |
| Subjects: | |
| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-05195-1 |
| Summary: | Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of Franȯis Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author<U+0019>s H-measures, variants by Patrick Gřard, and others yet to be discovered. |
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| Physical Description: | XXII, 471p. online resource. |
| ISBN: | 9783642051951 |
| ISSN: | 1862-9113 ; |