Diffusion-approximation in stochastically forced kinetic equations | Zendy

Arnaud Debussche | Zendy; Julien Vovelle | Zendy

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Diffusion-approximation in stochastically forced kinetic equations

Author(s) -

Arnaud Debussche,

Julien Vovelle

Publication year - 2020

Publication title -

tunisian journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 2576-7666

pISSN - 2576-7658

DOI - 10.2140/tunis.2021.3.1

Subject(s) - fokker–planck equation , stochastic differential equation , boltzmann equation , scalar (mathematics) , statistical physics , limit (mathematics) , mathematics , diffusion equation , diffusion , physics , diffusion process , partial differential equation , vlasov equation , anomalous diffusion , mathematical analysis , electron , quantum mechanics , knowledge management , geometry , economy , innovation diffusion , computer science , economics , service (business)

We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and short-range correlation. In the scales and the regime we consider, the hydrodynamic equation is a scalar second-order stochastic partial differential equation. Compared to the deterministic case, we also observe a phenomenon of enhanced diffusion.

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