  We present solutions to the relativistic thin disc evolutionary equation
using an ${\alpha}$-model for the turbulent stress tensor. Solutions with a
finite stress at the innermost stable circular orbit (ISCO) give rise to
bolometric light curves with a shallow power law time dependence, in good
agreement with those observed in tidal disruption events. A self-similar model
based on electron scattering opacity, for example, yields a power law index of
$-11/14$, as opposed to $-19/16$ for the case of zero ISCO stress. These
solutions correspond to an extended period of relaxation of the evolving disc
which, like the light curves they produce, is not sustainable indefinitely.
Cumulative departures from the approximation of exact circular orbits cause the
power law index to evolve slowly with time, leading eventually to the steeper
fall-off associated with traditional zero ISCO stress models. These modified
solutions are discussed in detail in a companion paper.
