Elliptic and Parabolic Equations - Abstract

Kopfova, Jana

Uniqueness and asymptotic behaviour for a class of parabolic partial differential equations with hysteresis and convection

We will deal with the question of existence, uniqueness and asymptotic behaviour of solutions of a parabolic equation with convection and Preisach hysteresis nonlinearity. This equation is a part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates. The key point in the uniqueness proof is to get enough regularity for the gradient of the hysteresis term and then apply a discrete version of Moser iteration lemma.