Asymptotic behaviour of evolution equations involving outwards pointing hysteresis operators

The paper deals with the long-time behaviour of evolution systems involving hysteresis operators. Introducing the concept of outwards pointing hysteresis operators allows to generalize methods that have been used to derive uniform a priori bounds for solutions to equations involving the superposition with nonlinear functions. This is done to derive a large-time asymptotic result for a coupled system of PDEs and ODEs modelling nonlinear thermo-visco-plastic developments. Moreover, a class of generalized Prandtl-Ishlinskii operator will be introduced and results concerning the thermodynamic consistency and the outwards pointing property of these operators will be presented