Seminar Abstracts
*Augusto Visintin*, Universita' degli Studi di Trento, Dipartimento diMatematica, Trento, Italy.

**TITLE**: "Quasilinear Equations with Hysteresis"

**ABSTRACT**: Let be a hysteresis operator,
and *A* a second order elliptic operator.
The following equation arises in
elasto-plasticity, ferromagnetism, ferroelectricity:

For equal to a (possibly discontinuous) scalar Preisach
operator, existence of a solution is proved for an
associated initial- and boundary-value problem.

Processes in ferromagnetic metals and in ferromagnetic insulators
can be represented by the following vector equations,
respectively,

(here written with normalized coefficients).

Existence of a solution is proved for an initial- and
boundary-value problem associated to (2), for
equal to a
(possibly discontinuous) vector estension of the Preisach operator.

A similar result is proved for (3),
for a smaller class of (discontinuous) hysteresis operators.