FRIDAY, September 1, 2000

CNA/MATH COLLOQUIUM: 4:30 P.M., WeH 7500, Augusto Visintin, Universita’ degli Studi di Trento, Dipartimento diMatematica, Trento, Italy. TITLE: ”Quasilinear Equations with Hysteresis” ABSTRACT: Let F be a hysteresis operator, and A a second order elliptic operator. The following equation arises in elasto-plasticity, ferromagnetism, ferroelectricity:

\frac{∂^{2}}{∂t^{2}} [u + F(u)] + Au = f.  (1)

For F 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,

\frac{∂}{∂t}[H⃗ + F⃗(H⃗) + ∇ × ∇ × H⃗ = f⃗,  (2)

\frac{∂^{2}}{∂t^{2}} [H⃗ + F⃗(H⃗)] + ∇ × ∇ × H⃗ = f⃗  (3)

(here written with normalized coefficients). Existence of a solution is proved for an initial- and boundary-value problem associated to (2), for F⃗ 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.