  It is shown that if the initial condition of the Cauchy problem for the
diffusion equation on a general infinite countable ultrametric space is
spherically symmetric with respect to some point, then this problem has an
exact analytical solution. A general solution of this problem is presented for
pure ultrametric diffusion, as well as for ultrametric diffusion with a
reaction sink concentrated at the center of spherical symmetry. Conditions on
the ultrametric and the distribution of the number of states in ultrametric
spheres are found that lead at large times to the asymptotic behavior of the
solutions obtained in the form of a power law modulated by a bounded function
that is log-periodic under some additional conditions.
