Ordinary Dierential Equations Research Articles

Semilinear parabolic equations with Preisach hysteresis

A coupled system consisting of a semilinear parabolic partial dierential equation and a family of ordinary dierential equations which is capable of modeling a very general class of hysteresis eects will be realized as an abstract Cauchy problem. Accretiveness estimates and maximality conditions are established in a product of L 1 spaces for the closure of the operator associated with this problem. Thus, the Cauchy problem corresponding to the closed operator admits a unique integral solution by way of the Crandall-Liggett theory. Special cases of the system include a one-dimensional derivation from Maxwell’s equations for a ferromagnetic body under slowly varying field conditions, the Super-Stefan problem, and other partial dierential equations with hysteresis terms appearing in the literature.