Magnetic diffusion, which is always coupled by Ohmic heating, is one of the dominate effects in the high-power pulsed current loaded experiments. The Ohmic heating can make the magnetic diffusion coefficient (i. e., the resistivity) vary violently, and make the diffusion a highly nonlinear process. For this reason, the problem is normally very hard to be solved analytically. Under the condition of a step-function resistivity, we successfully derived an exact solution for this nonlinear problem. This report introduces the derivation process of the exact solution and analyzes the characteristics of the solution.
 

magnetic diffusion, Ohmic heating, exact solution, PDE, step-function resisitivity model