  We study the Josephson plasma resonance (JPR) in
Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$ (BSCCO) with spatially dependent interlayer-phase
coherence (IPC). The half-irradiated BSCCO (HI-BSCCO), in which columnar
defects are introduced only in a half of the sample, shows several resonance
peaks, which are not simple superposition of the peaks in irradiated- and
pristine-parts. JPR in HI-BSCCO changes its character from irradiated- to
pristine-type at a crossover frequency ($\omega_{cr}$). We demonstrate that the
one-dimensional \LSGE, which takes into account the spatial dependence of IPC,
can reproduce most of the experimental findings including the presence of
$\omega_{cr}$.
