GEOMETRIC TWO-SCALE CONVERGENCE ON MANIFOLD AND APPLICATIONS TO THE VLASOV EQUATION. - Archive ouverte HAL
Journal Articles Discrete and Continuous Dynamical Systems - Series S Year : 2015

GEOMETRIC TWO-SCALE CONVERGENCE ON MANIFOLD AND APPLICATIONS TO THE VLASOV EQUATION.

Abstract

We develop and we explain the two-scale convergence in the covariant formalism, i.e. using di erential forms on a Riemannian manifold. For that purpose, we consider two manifolds M and Y , the rst 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.

Domains

Functional Analysis [math.FA] Differential Geometry [math.DG] Analysis of PDEs [math.AP] Numerical Analysis [math.NA]
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https://hal.science/hal-00833192

Submitted on : Tuesday, June 18, 2013-9:48:07 AM

Last modification on : Monday, May 6, 2024-6:58:02 PM

Long-term archiving on : Tuesday, April 4, 2017-7:50:48 PM

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hal-00833192 , version 1 (18-06-2013)

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  • HAL Id : hal-00833192 , version 1

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Aurore Back, Emmanuel Frenod. GEOMETRIC TWO-SCALE CONVERGENCE ON MANIFOLD AND APPLICATIONS TO THE VLASOV EQUATION.. Discrete and Continuous Dynamical Systems - Series S, 2015, Special Issue on "Numerical Methods Based on Two-Scale Convergence and Homogenization", 8 (1), pp 223--241. ⟨hal-00833192⟩

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