HETEROGENEOUS DISCRETE KINETIC MODEL AND ITS DIFFUSION LIMIT

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A revertible discrete velocity kinetic model is introduced when the environment is spatially heterogeneous. It is proved that the parabolic scale singular limit of the model exists and satisfies a new heterogeneous diffusion equation that depends on the diffusivity and the turning frequency together. An energy functional is introduced which takes into account spatial hetero-geneity in the velocity field. The monotonicity of the energy functional is the key to obtain uniform estimates needed for the weak convergence proof. The Div-Curl lemma completes the strong convergence proof.
Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
Issue Date
2021-10
Language
English
Article Type
Article
Citation

KINETIC AND RELATED MODELS, v.14, no.5, pp.749 - 765

ISSN
1937-5093
DOI
10.3934/krm.2021023
URI
http://hdl.handle.net/10203/288598
Appears in Collection
MA-Journal Papers(저널논문)
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