WIAS Preprint No. 678, (2001)

Singular limit in parabolic differential inclusions and the stop operator


  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 35K85 35B25 47J40


  • Parabolic differential inclusion, singular limit, hysteresis operators, penalty approximation, phase transitions




Parabolic differential inclusions with convex constraints in a finite-dimensional space are considered with a small "diffusion" coefficient ε in the elliptic term. This problem arises for instance in multicomponent phase-field systems. We prove the strong convergence of solutions as ε → 0 to the solution of the singular limit equation and show the connection to elementary hysteresis operators.

Appeared in

  • Interfaces and Free Boundaries, 4 (2002), pp. 423-435

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