Geometric two-scale convergence on manifold and applications to the Vlasov equation

Aurore Back; Emmanuel Frénod

doi:10.3934/dcdss.2015.8.223

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2015, Volume 8, Issue 1: 223-241. Doi: 10.3934/dcdss.2015.8.223

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Geometric two-scale convergence on manifold and applications to the Vlasov equation

Aurore Back^1, and
Emmanuel Frénod^2,

1.
Centre de physique théorique-CNRS, Campus de Luminy, Case 907 13288 Marseille cedex 9
2.
LMBA (UMR 6205) Université de Bretagne-Sud, Campus de Tohannic, 56000 Vannes

Received: April 30, 2013

Revised: August 31, 2013

Published: January 2015

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Abstract

We develop and we explain the two-scale convergence in the covariant formalism, i.e. using differential forms on a Riemannian manifold. For that purpose, we consider two manifolds $M$ and $Y$, the first one contains the positions and the second one the oscillations. We establish some convergence results working on geodesics on a manifold. Then, we apply this framework on examples.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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