Young measure solutions of a class of forward–backward diffusion equations

Abstract This paper is devoted to Young measure solutions of a class of forward–backward diffusion equations. Inspired by the idea from a recent work of Demoulini, we first discuss the regular case by introducing the Young measure solutions and prove the existence for such solutions, and then approximate the extreme case by the approach of regularization and establish the existence of Young measure solutions in the class of functions with bounded variation.

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