  In the regime of lubrication approximation, we look at spreading phenomena
under the action of singular potentials of the form $P(h)\approx h^{1-m}$ as
$h\to 0^+$ with $m>1$, modeling repulsion between the liquid-gas interface and
the substrate. We assume zero slippage at the contact line. Based on formal
analysis arguments, we report that for any $m>1$ and any value of the speed
(both positive and negative) there exists a three-parameter, hence generic,
family of fronts (i.e., traveling-wave solutions with a contact line). A
two-parameter family of advancing "linear-log" fronts also exists, having a
logarithmically corrected linear behaviour in the liquid bulk. All these fronts
have finite rate of dissipation, indicating that singular potentials stand as
an alternative solution to the contact-line paradox. In agreement with steady
states, fronts have microscopic contact angle equal to $\pi/2$ for all $m>1$
and finite energy for all $m<3$. We also propose a selection criterion for the
fronts, based on thermodynamically consistent contact-line conditions modeling
friction at the contact line. So as contact-angle conditions do in the case of
slippage models, this criterion selects a unique (up to translation) linear-log
front for each positive speed. Numerical evidence suggests that, fixed the
speed and the frictional coefficient, its shape depends on the spreading
coefficient, with steeper fronts in partial wetting and a more prominent
precursor region in dry complete wetting.
