The nonlinear and nonlocal diffusion equation for the relaxing current density J(r,t) in long superconductors of arbitrary cross section in a constant perpendicular magnetic field Bₐ is solved exactly by separation of variables in the electric field E(r,t)0ex0ex=0ex0exf(r)g(t). This solution includes the limiting cases of longitudinal and transverse geometries and applies to the current-voltage laws E∝Jⁿ ranging from Ohmic ( n0ex0ex=0ex0ex1) to Bean-like ( n→∞) behavior. The electric field profile f(r) weakly depends on n and becomes universal for n exceeding ≈5. At large times t one finds E∝1/t^n/(n-1) and J∝1/t^1/(n-1) for $n>1$, and E∝J∝exp(-t/τ₀) for n0ex0ex=0ex0ex1. The contour lines of the creeping E(r,t) coincide with the field lines of B(r,t) in the remanent state Bₐ0ex0ex=0ex0ex0.
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Ernst Helmut Brandt (1996) studied this question.