  We study the gravothermal evolution of dark matter halos in the presence of
dissipative dark matter self-interactions. Dissipative interactions are present
in many particle-physics realizations of the dark-sector paradigm and can
significantly accelerate the gravothermal collapse of halos compared to purely
elastic dark matter self-interactions. This is the case even when the
dissipative interaction timescale is longer than the free-fall time of the
halo. Using a semianalytical fluid model calibrated with isolated and
cosmological $N$-body simulations, we calculate the evolution of the halo
properties -- including its density profile and velocity dispersion profile --
as well as the core-collapse time as a function of the particle model
parameters that describe the interactions. A key property is that the inner
density profile at late times becomes cuspy again. Using 18 dwarf galaxies that
exhibit a corelike dark matter density profile, we derive constraints on the
strength of the dissipative interactions and the energy loss per collision.
