On the branching of singularities in complex domains
type: Item
instance of: scholarly article
title: On the branching of singularities in complex domains
zbMATH Open document ID: 0831.35004
author: Katasuju Igari
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-12-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35G10
zbMATH DE Number: 701466
zbMATH Keywords: branching of singularities
MaRDI profile type: Publication
full work available at URL: pjaa.70.128
OpenAlex ID: W1998197152
cites work: Systemes d'équations aux dérivées partielles à caractéristiques multiples: problème de Cauchy ramifie, hyperbolicite partielle
cites work: Characteristic Cauchy problems and analytic continuation of holomorphic solutions
cites work: Q3739533
cites work: Q3966494
cites work: Ramiflication of the solutions of the Cauchy problem for a special second order equation with singular data
cites work: Hamada's theorem for a certain type of the operators with double characteristics
cites work: Problème de Cauchy ramifié pour une classe d'opérateurs a caractéristiques tangentes. I. (Ramified Cauchy problems for a class of operators with tangential characteristics. I)
DOI: 10.3792/PJAA.70.128
description: scientific article; zbMATH DE number 701466