Asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping. II
type: Item
instance of: scholarly article
title: Asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping. II
zbMATH Open document ID: 0962.35124
author: Huijiang Zhao
published in: Journal of Differential Equations
publication date: 2001-06-05T00:00:00Z
review text: The paper follows the work of \textit{K. Nishihara} [J. Differ. Equations 137, No. 2, 384-395 (1997; Zbl 0881.35076)] in treating the Cauchy problem for the quasilinear hyperbolic equation \(V_{tt}-a(V_x)_x+V_t=0.\) A similar decay property of the solution is proved under weaker assumptions on smallness of the initial data. Under additional assumptions on the nonlinear term \(a(v),\) the solution to the linearized problem is still an asymptotic profile of \(V(t,x).\)
reviewed by: Marie Kopáčková
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 1545275
zbMATH Keywords: asymptotic profile
zbMATH Keywords: a priori estimate
zbMATH Keywords: smallness of the initial data
MaRDI profile type: Publication
full work available at URL: jdeq.2000.3793
OpenAlex ID: W1983316458
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DOI: 10.1006/JDEQ.2000.3793
description: scientific article; zbMATH DE number 1545275