Parabolic differential inclusions with convex constraints in a finite-dimensional space are considered with a small 'diffusion' coefficient [egr] at the elliptic term. This problem arises for instance in multicomponent phase-field systems. We prove the strong convergence of solutions as [egr] [rarr] 0 to the solution of the singular limit equation and show the connection to elementary hysteresis operators.
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Jürgen Sprekels, Pavel Krejčí, Parabolic regularization of differential inclusions and the stop operator. Interfaces Free Bound. 4 (2002), no. 4, pp. 423–435DOI 10.4171/IFB/68