On some P.D.E.s with hysteresis

The aim of this thesis is to present some results concerning some new classes of P.D.E.s containing a continuous hysteresis operator. Even if in the most frequent applications the operators involved in our treatment will be also rate independent, our results turn to be valid for the more general class of memory operators. Throughout the text, we focus our attention on the well-posedness of our model problems, dealing, when possible, with several kind of boundary conditions; in the last chapter, we present instead a result of asymptotic behaviour.