  The local Cosmic Ray (CR) energy spectrum exhibits a spectral softening at
energies around 3~PeV. Sources which are capable of accelerating hadrons to
such energies are called hadronic PeVatrons. However, hadronic PeVatrons have
not yet been firmly identified within the Galaxy. Several source classes,
including Galactic Supernova Remnants (SNRs), have been proposed as PeVatron
candidates. The potential to search for hadronic PeVatrons with the Cherenkov
Telescope Array (CTA) is assessed. The focus is on the usage of very high
energy $\gamma$-ray spectral signatures for the identification of PeVatrons.
Assuming that SNRs can accelerate CRs up to knee energies, the number of
Galactic SNRs which can be identified as PeVatrons with CTA is estimated within
a model for the evolution of SNRs. Additionally, the potential of a follow-up
observation strategy under moonlight conditions for PeVatron searches is
investigated. Statistical methods for the identification of PeVatrons are
introduced, and realistic Monte--Carlo simulations of the response of the CTA
observatory to the emission spectra from hadronic PeVatrons are performed.
Based on simulations of a simplified model for the evolution for SNRs, the
detection of a $\gamma$-ray signal from in average 9 Galactic PeVatron SNRs is
expected to result from the scan of the Galactic plane with CTA after 10 hours
of exposure. CTA is also shown to have excellent potential to confirm these
sources as PeVatrons in deep observations with $\mathcal{O}(100)$ hours of
exposure per source.
