NONLINEAR DIFFUSION IN HARD AND SOFT SUPERCONDUCTORS

We discuss the diffusion of magnetic flux in a field-cooled (''hard'') superconducting slab in a creep regime in which E proportional to \J\(sigma)J. Bryksin and Dorogovtsev recently discussed flux diffusion in a pinningless (''soft'') superconductor in which E proportional to \B\J. This problem is closely related to the flux-creep one with sigma=1, and provides additional insight into the possible types of behaviour. We list a series of possible long-term asymptotic solutions of a scaling form, which are either analytically exact or accurately calculated. We check numerically that the relevant long-term solution is approached after various initial conditions. Amongst other conclusions we find S=d(1n\M\)/d(1n t)-->-1/sigma or -1/2 sigma, after application and removal of an additional field, according to whether the disturbance has reached the sample centre or not. A relaxing sandpile model appears to have wide validity when creep is only a small correction to the critical state, as when sigma-->infinity.