Singular limit in parabolic differential inclusions and the stop operator
- Krejčí, Pavel
- Sprekels, Jürgen
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.
- Interfaces and Free Boundaries, 4 (2002), pp. 423-435