  By analyzing breathing mode of a Bose-Einstein condensate repulsively
interacting with a polarized fermionic cloud, we further the understanding of a
Bose-Fermi mixture recently realized by Lous et al. [\textit{Phys. Rev. Lett.}
\textbf{120}, 243403]. We show that a hydrodynamic description of a domain wall
between bosonic and fermionic atoms reproduces experimental data of Huang et
al. [\textit{Phys. Rev. A} \textbf{99}, 041602(R)]. Two different types of
interaction renormalization are explored, based on lowest order constrained
variational and perturbation techniques. In order to replicate nonmonotonic
behavior of the oscillation frequency observed in the experiment, temperature
effects have to be included. We find that the frequency down-shift is caused by
the fermion-induced compression and rethermalization of the bosonic species as
the system is quenched into the strongly interacting regime.
