Mathematical Models of Hysteresis

Abstract

This chapter is a survey of past and ongoing research on mathematical modeling of hysteresis phenomena. It concentrates on three phenomena of relevant physical and engineering interest: hysteresis in continuum mechanics, in ferromagnetism, and in filtration through porous media. The chapter reviews some general features of elasto-plasticity and micromagnetism, and introduces a mathematical model of hysteresis in filtration through porous media. The outcome of most of these models consists of PDEs that include hysteresis nonlinearities. This chapter studies some parabolic and hyperbolic PDEs that contain hysteresis operators. The chapter illustrates that hysteresis can be generated through feedback and nonmonotonicity, and discusses how hysteresis may arise in space-distributed systems.