  In this paper we study the spherically symmetric characteristic initial data
problem for the Einstein-Maxwell-scalar field system with a positive
cosmological constant in the interior of a black hole, assuming an exponential
Price law along the event horizon. More precisely, we construct open sets of
characteristic data which, on the outgoing initial null hypersurface (taken to
be the event horizon), converges exponentially to a reference
Reissner-N\"{o}rdstrom black hole at infinity.
  We prove the stability of the radius function at the Cauchy horizon, and show
that, depending on the decay rate of the initial data, mass inflation may or
may not occur. In the latter case, we find that the solution can be extended
across the Cauchy horizon with continuous metric and Christoffel symbols in
$L^2_{{\rm loc}}$, thus violating the Christodoulou-Chru\'sciel version of
strong cosmic censorship.
