JournalsifbVol. 4 , No. 4DOI 10.4171/ifb/68

Parabolic regularization of differential inclusions and the stop operator

  • Jürgen Sprekels

    Angewandte Analysis und Stochastik, Berlin, Germany
  • Pavel Krejcí

    Academy of Sciences, Praha, Czech Republic
Parabolic regularization of differential inclusions and the stop operator cover

Abstract

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.