On the branching of singularities in complex domains
It is known that the singularities of the solution of the Cauchy problem in complex domains are generally contained in the union of the characteristic hypersurfaces \(K_i\) issued from the singular support \(T\) of the initial data. But, usually, the singularities do not necessarily propagate onto all \(K_i\). In fact, it is also known that there are, in general, solutions with singularities on and only on a given characteristic hypersurface [see \textit{S. Ōuchi}, J. Fac. Sci., Univ. Tokyo, Sect. I A 32, 457-498 (1985; Zbl 0603.35014); and \textit{J. Persson}, Astérisque, 89-90, 223-247 (1981; Zbl 0501.35018)]. In this note, we consider a special class of operators of second order with tangent characteristics, and show that the singularities of the solution always propagate onto both \(K_1\) and \(K_2\). This is a complex version of the branching of singularities.
scientific article; zbMATH DE number 701466