  We study two-dimensional de Sitter universe which evolves and proliferates
according to the Ginsparg-Perry-Bousso-Hawking mechanism, using
Jackiw-Teitelboim gravity coupled to conformal matter. Black holes are
generated by quantum gravity effects from pure de Sitter space and then
evaporate to yield multiple disjoint de Sitter spaces. The back-reaction from
the matter CFT is taken into account for the dilaton as a function of the
temperature of the CFT. We discuss the evaporation of black holes and calculate
the finite temperature entropy of an inflating region using the island formula.
We find that the island moves towards the apparent horizon of the black hole as
the temperature increases. The results are applied to the case of multiple
evaporating black holes, for which we suggest multiple islands.
