Perfectly matched layers are an essential tool designed in the nineties for the computation of electromagnetic waves. The method replaces the Maxwell equations by a larger system, and introduce variable absorption coefficients that are nonvanishing near the boundary of the computational box. Classic absorbing conditions are imposed at the boundary. Well posedness of the resulting initial boundary value problem is proved here for the first time. The analysis proceeds by Laplace transform in time on smoothed domains. There we design boundary conditions for a non selfadjoint Helmholtz system. Estimates uniform in the smoothing are proved using carefully constructed test functions. One estimate is of energy type with less positivity than usual. A second follows Jerison-Kenig-Mitrea from elliptic problems in Lipschitz domains.