  Evaluating the completion time of a random algorithm or a running stochastic
process is a valuable tip not only from a purely theoretical, but also
pragmatic point of view. In the formal sense, this kind of a task is specified
in terms of the first-passage time statistics. Although first-passage
properties of diffusive processes, usually modeled by different types of the
linear differential equations, are permanently explored with unflagging
intensity, there still exists noticeable niche in this subject concerning the
study of the non-linear diffusive processes. Therefore, the objective of the
present paper is to fill this gap, at least to some extent. Here, we consider
the non-linear diffusion equation in which a diffusivity is power-law dependent
on the concentration/probability density, and analyse its properties from the
viewpoint of the first-passage time statistics. Depending on the value of the
power-law exponent, we demonstrate the exact and approximate expressions for
the survival probability and the first-passage time distribution along with its
asymptotic representation. These results refer to the freely and harmonically
trapped diffusing particle. While in the former case the mean first-passage
time is divergent, even though the first-passage time distribution is
normalized to unity, it is finite in the latter. To support this result, we
derive the exact formula for the mean first-passage time to the target
prescribed in the minimum of the harmonic potential.
