  An exact solution of the nonlinear nonlocal diffusion problem is obtained
that describes the evolution of the magnetic flux injected into a soft or hard
type-II superconductor film or a two-dimensional Josephson junction array. (The
magnetic field in vortices is assumed to be perpendicular to the film; the
electric field induced by the vortex motion is proportional to the local
magnetic induction; flux creep in the hard superconductors under consideration
is described by the logarithmic U(j) dependence.) Self-similar flux
distributions with sharp square-root fronts are found. The fronts are shown to
expand with power law time-dependence. A sharp peak in the middle of the
distribution appears in the hard superconductor case.
