Propagation of Gevrey singularities for equations of principal type satisfying condition (P) (Q1847605)

The authors investigate the propagation of singularities in Gevrey class for the first-order operator \(P= D_t+ iF(t,x,D)\) of principal type satisfying the condition \((P)\). They prove that if the coefficients of equations belong to the Gevrey class of index \(s'\), and \(\gamma(\partial I)\cap WF_s(u)= \emptyset\) and \(\gamma(I)\cap WF_s(Pu)=\emptyset\) hold, then \(\gamma(I)\cap WF_s(u)= \emptyset\) for \(s'\geq 2\) and \(s\geq s'+ 2\), where \(\gamma\) is the Hamilton flow associated to \(F\) and \(I\) is an interval.