Semilinear Parabolic Equations with Preisach Hysteresis
Abstract
A coupled system consisting of a nonlinear parabolic partial differential equation and a family of ordinary differential equations is realized as an abstract Cauchy problem. We establish coercivity and accretiveness estimates for the multivalued operator in the abstract Cauchy problem, and then apply the CrandallLiggett theorem to recover the integral solution for the abstract Cauchy problem. A special case of the coupled system corresponds to the Super Stefan problem, i.e. the delayed phase transition model for a material subjected to superheating and supercooling. In this case, the nonlinearity in the parabolic partial differential equation appears as the time derivative of a simple relay hysteresis functional produced by one member of the family of ordinary differential equations. Another special case of the coupled system corresponds to a onedimensional derivation from Maxwell's equations for a ferromagnetic body under slowly varying field conditions. In this case, the nonlinearity is the time derivative of the classical Preisach hysteresis functional, and the family of ordinary differential equations produce a family of simple relay hysteresis functionals present in the construction of the Preisach hysteresis functional.
 Publication:

Ph.D. Thesis
 Pub Date:
 1993
 Bibcode:
 1993PhDT.......192L
 Keywords:

 ABSTRACT CAUCHY;
 Mathematics; Physics: Fluid and Plasma; Physics: Condensed Matter