Global existence for systems of nonlinear wave equations in two space dimensions
type: Item
instance of: scholarly article
title: Global existence for systems of nonlinear wave equations in two space dimensions
zbMATH Open document ID: 0830.35083
author: Soichiro Katayama
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1996-01-28T00:00:00Z
review text: The author considers the Cauchy problem for a system of fully nonlinear wave equations of the type \[ \square u_i = F_i (u,u',u'') \text{ in } \overline \mathbb{R}_+\times\mathbb{R}^n, \quad u_i (0,x) = \varepsilon f_i (x),\;\partial_t u_i (0,x) = \varepsilon g_i (x),\;x \in \mathbb{R}^n \] where \(n = 2\), and \(F = O (|u |^p + |u' |^p + |u'' |^p)\) with \(p = 3\). He proves the global existence of the classical solution under certain assumptions, following the method given in Klainerman's previous paper.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 562836
zbMATH Keywords: fully nonlinear wave equation
zbMATH Keywords: global existence
zbMATH Keywords: classical solution
reviewed by: Shuxing Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195166427
OpenAlex ID: W2160580709
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DOI: 10.2977/PRIMS/1195166427
description: scientific article; zbMATH DE number 562836