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Fast reaction limit and forward-backward diffusion: A Radon–Nikodym approach
Jakub Skrzeczkowski1 
1 Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Stefana Banacha 2, 02-097 Warsaw, Poland
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 189-203.

We consider two singular limits: a fast reaction limit with a non-monotone nonlinearity and a regularization of the forward-backward diffusion equation. We derive pointwise identities satisfied by the Young measure generated by these problems. As a result, we obtain an explicit formula for the Young measure even without the non-degeneracy assumption used in the previous works. The main new idea is an application of the Radon–Nikodym theorem to decompose the Young measure.

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DOI : 10.5802/crmath.279
Classification : 35K57, 35B25, 35B36
Jakub Skrzeczkowski 1

1 Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Stefana Banacha 2, 02-097 Warsaw, Poland
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     language = {en},
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Jakub Skrzeczkowski. Fast reaction limit and forward-backward diffusion: A Radon–Nikodym approach. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 189-203. doi : 10.5802/crmath.279. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.279/

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