A remark on global smooth solutions for quasilinear wave equations
type: Item
instance of: scholarly article
title: A remark on global smooth solutions for quasilinear wave equations
zbMATH Open document ID: 0809.35059
author: Renato Manfrin
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1994-10-09T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108318
review text: Summary: Following a result of S. Klainerman, we prove the existence of global smooth solutions in \(\mathbb{R}_ t\times \mathbb{R}_ x^ n\) for quasilinear wave equations with small initial data which are periodic in at most \(n- 2\) variables. The proof is based on suitable decay estimates for partially periodic solutions of the homogeneous wave equation.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 627419
zbMATH Keywords: global smooth solutions
zbMATH Keywords: decay estimates
MaRDI profile type: Publication
cites work: Q3266592
cites work: Q3240445
cites work: Q5679204
cites work: Q3843844
cites work: \(L^ p\)-decay rates for homogeneous wave-equations
cites work: Uniform decay estimates and the lorentz invariance of the classical wave equation
cites work: Global existence for nonlinear wave equations
cites work: Global, small amplitude solutions to nonlinear evolution equations
cites work: Initial value problems for nonlinear wave equations
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description: scientific article; zbMATH DE number 627419