Evolution of semilinear waves with swallowtail singularities
type: Item
instance of: scholarly article
title: Evolution of semilinear waves with swallowtail singularities
zbMATH Open document ID: 0827.35078
DOI: 10.1215/S0012-7094-94-07520-0
author: Antonio Sá Barreto
published in: Duke Mathematical Journal
publication date: 1995-12-18T00:00:00Z
review text: The author considers the formation of caustics for bounded solutions of a semilinear wave equation \(Pu = f(z,u)\), \(z \in \Omega \subset \mathbb{R}^n\), \(f\) smooth, with \(P\) a second order strictly hyperbolic differential operator, and shows that in the case of the swallowtail caustic and conormal initial data the only additional singularities of the solution \(u\) due to the nonlinearity of the equation lie on the forward characteristic cone over the swallowtail tip. Firstly the formation of caustics for the linear wave equation is considered. Then many propositions and theorems are demonstrated after introduction of a family of spaces \(J_K (\Omega)\), \(K \in\mathbb{N}\), satisfying particular algebraical conditions.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 706701
zbMATH Keywords: semilinear wave equation
zbMATH Keywords: swallowtail caustic
reviewed by: Silvio Nocilla
MaRDI profile type: Publication
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full work available at URL: s0012-7094-94-07520-0
OpenAlex ID: W2082805242
description: scientific article; zbMATH DE number 706701