  We present Gran Telescopio CANARIAS CanariCam 8.7$\mu$m imaging and
7.5-13$\mu$m spectroscopy of six local systems known to host an active galactic
nucleus (AGN) and have nuclear star formation. Our main goal is to investigate
whether the molecules responsible for the 11.3$\mu$m polyclyclic aromatic
hydrocarbon (PAH) feature are destroyed in the close vicinity of an AGN. We
detect 11.3$\mu$m PAH feature emission in the nuclear regions of the galaxies
as well as extended PAH emission over a few hundred parsecs. The equivalent
width (EW) of the feature shows a minimum at the nucleus but increases with
increasing radial distances, reaching typical star-forming values a few hundred
parsecs away from the nucleus. The reduced nuclear EW are interpreted as due to
increased dilution from the AGN continuum rather than destruction of the PAH
molecules. We conclude that at least those molecules responsible for the
11.3$\mu$m PAH feature survive in the nuclear environments as close as 10pc
from the AGN and for Seyfert-like AGN luminosities. We propose that material in
the dusty tori, nuclear gas disks, and/or host galaxies of AGN is likely to
provide the column densities necessary to protect the PAH molecules from the
AGN radiation field.
