Exact solutions and branching of singularities for some hyperbolic equations in two variables
type: Item
instance of: scholarly article
title: Exact solutions and branching of singularities for some hyperbolic equations in two variables
zbMATH Open document ID: 1172.35304
author: Yakar Kannai
author: Richard Beals
published in: Journal of Differential Equations
publication date: 2009-05-19T00:00:00Z
review text: The authors refer to the Cauchy problem for singular hyperbolic operators with a lower order term depending on a parameter, considered in [\textit{F. Trèves}, Proc. Am. Math. Soc. 46, 229--233 (1974; Zbl 0297.35048)]. Using the methodology and their earlier results from [\textit{R. Beals, Y. Kannai}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 464, No. 2092, 795--806 (2008; Zbl 1142.44001)] they extend the non-uniqueness result from Trèves and prove branching and non-branching of singularities results. The degenerate hyperbolic case is considered too.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35L80
zbMATH DE Number: 5555265
zbMATH Keywords: singular hyperbolic operator
zbMATH Keywords: degenerate hyperbolic operator
zbMATH Keywords: uniqueness Cauchy problem
zbMATH Keywords: branching of singularities
zbMATH Keywords: branching and non-branching
MaRDI profile type: Publication
full work available at URL: j.jde.2009.02.023
OpenAlex ID: W2027376340
cites work: Q3967891
cites work: Branching of singularities for degenerate hyperbolic operator and Stokes phenomena. IV
cites work: Branching of singularities for degenerate hyperbolic operators
cites work: Exact propagators for some degenerate hyperbolic operators
cites work: Inverse Laplace transforms of products of Whittaker functions
cites work: Explicit solutions for a characteristic Cauchy problem
cites work: On a class of pseudodifferential operators with double characteristics
cites work: Q5519365
cites work: On the Riemann-Green function
cites work: Q4065863
cites work: Q5827353
cites work: On a singular boundary value problem for the Euler-Darboux equation
cites work: ON A CLASS OF ELLIPTIC PSEUDODIFFERENTIAL OPERATORS DEGENERATE ON A SUBMANIFOLD
cites work: Q4201211
cites work: On the propagation of singularities with infinitely many branching points for a hyperbolic equation of second order
cites work: Wave fronts of solutions of certain pseudodifferential equations
cites work: Q5781389
cites work: Fundamental solution for a hyperbolic equation with involutive characteristics of variable multiplicity
cites work: Propagation of singularities and uniqueness in the cauchy problem at a class of doubly characteristic points
cites work: A canonical form of a system of microdifferential equations with non- involutory characteristics and branching of singularities
cites work: Q3794610
cites work: Branching of singularities for a degenerate hyperbolic system
cites work: Q5665780
cites work: Q3882843
cites work: Concatenations of second‐order evolution equations applied to local solvability and hypoellipticity
cites work: Discrete Phenomena in Uniqueness in the Cauchy Problem
DOI: 10.1016/J.JDE.2009.02.023
description: scientific article; zbMATH DE number 5555265