Nonstrictly hyperbolic nonlinear systems
type: Item
instance of: scholarly article
title: Nonstrictly hyperbolic nonlinear systems
zbMATH Open document ID: 0614.35060
DOI: 10.1007/BF01457361
author: Walter Craig
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164247
review text: The initial value problem for a class of nonlinear hyperbolic systems is addressed in this paper, with initial data given in a Sobolev space of functions. These systems are not required to be strictly hyperbolic nor symmetrizable, and the admissible class includes systems with multiple characteristics. The fundamental requirement is a sign condition on the subprincipal operator of the linearized problem; this is parallel to a familiar condition for linear hyperbolic systems. Finally, the classical problem of water waves is shown to be related to this class of systems.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 3994132
zbMATH Keywords: well posedness
zbMATH Keywords: initial data
zbMATH Keywords: Sobolev space
zbMATH Keywords: multiple characteristics
zbMATH Keywords: subprincipal operator
zbMATH Keywords: linearized problem
zbMATH Keywords: water waves
MaRDI profile type: Publication
cites work: Singular nonlinear Cauchy problems
cites work: An existence theory for water waves and the boussinesq and korteweg-devries scaling limits
cites work: The multiplicity of eigenvalues
cites work: Equations hyperboliques non-strictes: Contre-examples du type De Giorgi, aux théoremes d'existence et d'unicité
cites work: Équations et systèmes non-linéaires, hyperboliques non-stricts
cites work: Q5520417
cites work: An abstract form of the nonlinear Cauchy-Kowalewski theorem
cites work: A note on a theorem of Nirenberg
cites work: Gravity waves on the free surface of an incompressible perfect fluid of finite depth
description: scientific article; zbMATH DE number 3994132