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We consider two singular limits: fast reaction limit with nonmonotonenonlinearity and regularization of forward-backward diffusion equation. It wasproved by Plotnikov that for cubic-type (nondegenerate) nonlinearities, thelimit oscillates between at most three states. In this paper we make hisargument more optimal and we sharpen the previous result: we use Radon-Nikodymtheorem to obtain a pointwise identity characterizing the Young measure. As aconsequence, we establish a simpler condition which implies Plotnikov resultfor piecewise affine functions. We also prove that the result is true if theYoung measure is not supported in the so-called unstable zone, the factobserved in numerical simulations.

Fast reaction limit and forward-backward diffusion: a Radon-Nikodym approach