\(L^{p}-L^{q}\) estimates for wave equations and the Kirchhoff equation
type: Item
instance of: scholarly article
title: \(L^{p}-L^{q}\) estimates for wave equations and the Kirchhoff equation
zbMATH Open document ID: 1157.35017
author: Tokio Matsuyama
published in: Osaka Journal of Mathematics
publication date: 2008-08-11T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ojm/1216151111
review text: The paper refers to the Cauchy problem for the wave equation with time-dependent coefficients. In case coefficients are of Lipschitz class, are assumed to satisfy some additional conditions and norms of data are finite, a decay estimate for solution is obtained. As technique one applies Fourier transform to the wave equation and initial data and one develops the asymptotic integration of the ODE. As an application, using the fixed point theorem of Schauder, estimates for the solution of Kirchhoff equation are determined.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 5309639
zbMATH Keywords: wave equation
zbMATH Keywords: decay estimate
zbMATH Keywords: Fourier transform
zbMATH Keywords: Kirchhiff equation
zbMATH Keywords: fixed point theorem of Schauder
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5309639