Note on discrete phenomena in uniqueness in doubly characteristic Cauchy problems (Q2494641)

The present study deals with the uniqueness in the Cauchy problem at doubly characteristic points. More precisely, let \(P(x,\partial)\) be a partial differential operator of order \(m\) with anaytic coefficients in an open set \(\Omega\) in \(\mathbb{R}^n\), the coefficients of its principal part \(P_m(x,\partial)\) be real-valued. The author addresses the following question: If \(P\) is doubly characteristic at \((x_0,\nu)\) and there are two bicharacterstic strip issued from \((x_0,\nu)\), how does the uniqueness depend on them?