Propagation and cancellation of singularities in a class of Fuchsian operators and their perturbations

Abstract

We obtain some new necessary conditions for wavefront propagation in the noninvolutive Fuchsian operator classt∂2/∂t2+λ(x,Dx)∂/∂t+β(x,Dx). The point of view here is to show that cancellation of propagation of a new singularity in some semilinear systems can be arranged by means of Fuchsian perturbation admitting exact (left and right) microlocal parametrices.