  BaTiO$_3$ (BTO) is a prototypical perovskite ferroelectric, whose dielectric
permittivity and loss spectra -- which are strongly temperature and frequency
dependent -- include contributions from inhomogeneous polarization patterns,
with polar domain walls (DWs) being the most common types. In order to
elucidate how DWs influence dielectric response, we utilized a continuum
approach based on the Landau-Ginzburg theory to model field-dependent
properties of polydomain tetragonal phase of BTO near room temperature and
above. A system with 180$^\circ$ DWs was evaluated as a case study, with both
position-resolved and volume-averaged dielectric susceptibility and loss
computed at different temperatures for a range of applied field frequencies and
amplitudes. Our results demonstrate that cooperative dipole fluctuations in the
vicinity of the DW provide a large (extrinsic) contribution to the system
dielectric response relative to the intrinsic contribution stemming from within
the domain. Dynamics of the DW profile fluctuations under applied field can be
represented by a combination of breathing and sliding vibrational motions, with
each exhibiting distinct dependence on the field frequency and amplitude. The
implications of this behavior are important for understanding and improving
control of coupled functional properties in ferroelectric materials, including
their dielectric, electromechanical, and electrooptical responses. Furthermore,
this investigation provides a computational benchmark for future studies and
can be readily extended to other topological polarization patterns in
ferroelectrics.
