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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Jakub Skrzeczkowski ^{1}

@article{CRMATH_2022__360_G2_189_0, author = {Jakub Skrzeczkowski}, title = {Fast reaction limit and forward-backward diffusion: {A} {Radon{\textendash}Nikodym} approach}, journal = {Comptes Rendus. Math\'ematique}, pages = {189--203}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.279}, language = {en}, }

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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