A one--dimensional model for the Barkhausen effect is considered. This model describes a motion in a random medium. The motion exhibits a stick--slip type behaviour in the limit of small correlation length of the random medium. However, we prove that the velocity of the limiting motion is positive almost everywhere. For this the corresponding Fokker--Planck equation is examined. This equation is degenerated and has a critical singularity as well as no gradient structure. Therefore, the proof relies mainly on choosing the right test functions, which gives natural boundary conditions in the limit.
"Barkhausen Effect: A Stick--Slip Motion in a Random Medium\." Methods Appl. Anal. 12 (1) 29 - 42, March 2005.