Longtime behavior of the hyperbolic equations with an arbitrary internal damping
type: Item
instance of: scholarly article
title: Longtime behavior of the hyperbolic equations with an arbitrary internal damping
zbMATH Open document ID: 1264.35041
author: Xiaoyu Fu
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2013-02-04T00:00:00Z
review text: For damped hyperbolic equations, IBV-problems with Neumann boundary conditions are considered. Assuming sharp regularity conditions, i.e. coefficients and boundary of class \(C^1\), logarithmic decay rate for solutions is proved. Results for \(C^2\) coefficients and domains with \(C^2\) boundary have been published by the author in a previous paper [Commun. Partial Differ. Equations 34, No. 9, 957--975 (2009; Zbl 1180.35104)]. The decay rate result is a consequence of a suitable resolvent estimate, which is proved by means of a global Carleman estimate and an interpolation inequality for elliptic equations with Neumann boundary conditions.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 6134351
zbMATH Keywords: logarithmic stability
zbMATH Keywords: interpolation inequatiliy
zbMATH Keywords: global Carleman estimate
zbMATH Keywords: resolvent operator
zbMATH Keywords: logarithmic decay rate
MaRDI profile type: Publication
full work available at URL: s00033-010-0113-0
OpenAlex ID: W2058312563
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DOI: 10.1007/S00033-010-0113-0
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description: scientific article; zbMATH DE number 6134351