The wave equation with a Preisach hysteresis operator can be considered as a one-dimensional projection of Maxwell" s equations in a ferromagnetic medium. An initial-boundary value problem for this equation is solved here with emphasizing the fact that under a bounded forcing term the solutions remain bounded. This is due to the strong dissipation of hysteresis energies. New proofs of hysteresis energy inequalities are given without referring to the structure of hysteresis memory
