Weak-convergence methods for Hamiltonian multiscale problems
We consider Hamiltonian problems depending on a small parameter like in wave equations with rapidly oscillating coefficients or the embedding of an infinite atomic chain into a continuum by letting the atomic distance tend to 0. For general semilinear Hamiltonian systems we provide abstract converge...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Berlin
WIAS
2007
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| Schriftenreihe: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik
1219 |
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Tag hinzufügen | Zusammenfassung: | We consider Hamiltonian problems depending on a small parameter like in wave equations with rapidly oscillating coefficients or the embedding of an infinite atomic chain into a continuum by letting the atomic distance tend to 0. For general semilinear Hamiltonian systems we provide abstract convergence results in terms of the existence of a family of joint recovery operators which guarantee that the effective equation is obtained by taking the [gamma]-limit of the Hamiltonian. The convergence is in the weak sense with respect to the energy norm. Exploiting the well-developed theory of [gamma]-convergence, we are able to generalize the admissible coefficients for homogenization in the wave equations. Moreover, we treat the passage from a discrete oscillator chain to a wave equation with general L∞ coefficients |
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| Beschreibung: | Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden. - Auch als gedr. Ausg. vorhanden Auch als elektronisches Dokument vorh |
| Beschreibung: | 31 S. 30 cm |