Semigroup Approach to the Question of Stability for a Partial Differential Equation with Hysteresis

A parabolic equation with hysteresis nonlinearity is studied. It is the purpose of this article to investigate the asymptotic behavior of the solution as tª`. A semigroup approach is used to show stability in L1 V.. Although this approach gives us slightly weaker results than known theorems in the case the hysteresis operator is the generalized play, it enables us to get stability results also for the Prandtl]Ishlinskii operator of play type and for some discontinuous hysteresis operators