Critical curve for \(p\)-\(q\) systems of nonlinear wave equations in three space dimensions
type: Item
instance of: scholarly article
title: Critical curve for \(p\)-\(q\) systems of nonlinear wave equations in three space dimensions
zbMATH Open document ID: 0977.35077
author: Rentaro Agemi
author: Y. Kurokawa
author: H. Takamura
published in: Journal of Differential Equations
publication date: 2001-03-13T00:00:00Z
review text: The Cauchy problem for \(p\)-\(q\) systems of nonlinear wave equations \(u_{tt}-\triangle u=|v|^{p}, v_{tt}-\triangle v=|u|^{q}\) in \(\mathbb{R}^{n}\times [0,+\infty)\) for small initial data is discussed. The authors prove a blow-up theorem for the nonlinearity \((p,q)\) being just on the critical curve in the case \(n=3.\) Moreover, the lower and upper bounds of the lifespan of solutions are precisely estimated, including the subcritical case.
reviewed by: Marie Kopáčková
Mathematics Subject Classification ID: 35L55
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B33
zbMATH DE Number: 1529995
zbMATH Keywords: lower and upper bounds of the lifespan
zbMATH Keywords: small initial data
zbMATH Keywords: blow-up theorem
zbMATH Keywords: a priori estimate
MaRDI profile type: Publication
full work available at URL: jdeq.2000.3766
OpenAlex ID: W1981311823
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DOI: 10.1006/JDEQ.2000.3766
description: scientific article; zbMATH DE number 1529995