  The study aims to examine the spectral dynamics of the low-frequency,
optically thick gyrosynchrotron microwave emission in solar flares to determine
the characteristics of the emitting source. We present the high-resolution
spectra of a set of microwave bursts observed by the Expanded Owens Valley
Solar Array (EOVSA) during its commissioning phase in the $2.5-18$ GHz
frequency range with $1$ second time resolution. Out of the 12 events analyzed
in this study, nine bursts exhibit a direct decrease with time in the optically
thick spectral index $\alpha_l$, an indicator of source morphology.
Particularly, five bursts display "flat" spectrum ($\alpha_l\leq1.0$) compared
to that expected for a homogeneous/uniform source ($\alpha_l\approx2.9$). These
flat spectra at the low-frequencies (<$10$ GHz) can be defined as the emission
from a spatially inhomogeneous source with a large area and/or with multiple
emission components. In a subset of six events with partial cross-correlation
data, both the events with flat spectra show a source size of $\sim120$ arcsec
at $2.6-3$ GHz. Modeling based on inhomogeneity supports the conclusion that
multiple discrete sources can only reproduce a flat spectrum. We report that
these flat spectra appear predominantly in the decay phase and typically grow
flatter over the duration in most of the bursts, which indicates the increasing
inhomogeneity and complexity of the emitting volume as the flare progresses.
This large volume of flare emission filled with the trapped energetic particles
is often invisible in other wavelengths, like hard X-rays, presumably due to
the collisionless conditions in these regions of low ambient density and
magnetic field strength.
