  This work is a contribution to the understanding of the question of stability
of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete
levels. First, stability results are presented for the Cartesian PMLs
associated to a general first-order hyperbolic system. Then, in the context of
the pressure-velocity formulation of the acoustic wave propagation, an unsplit
PML formulation is discretized with spectral mixed finite elements in space and
finite differences in time. It is shown, through the stability analysis of two
different schemes, how a bad choice of the time discretization can deteriorate
the CFL stability condition. Some numerical results are finally presented to
illustrate these stability results.
