  This work is devoted to the mathematical analysis of Stieltjes Bochner spaces
and their applications to the resolution of a parabolic equation with Stieltjes
time derivative. This novel formulation allows us to study parabolic equations
that present impulses at certain times or lapses where the system does not
evolve at all and presents an elliptic behavior. We prove several theoretical
results related to existence of solution, and propose a full algorithm for its
computation, illustrated with some realistic numerical examples related to
population dynamics.
