Energy estimates for a class of degenerate hyperbolic equations
type: Item
instance of: scholarly article
title: Energy estimates for a class of degenerate hyperbolic equations
zbMATH Open document ID: 1196.35146
author: Qing Han
published in: Mathematische Annalen
publication date: 2010-04-23T00:00:00Z
review text: Considered is the Cauchy problem for a linear degenerate inhomogeneous hyperbolic equation in one dimension. The leading coefficient which is allowed to vanish is decomposed in \(a(x ,t)= q(x ,t)K(x ,t)\), where \(K(x ,t)\), is a nonnegative smooth function and \(q(x ,t)\) is a positive smooth function. In case all coefficients are smooth functions on \(\mathbb R\times[0,T]\), \(K(x ,t)\) has real roots only and some additional conditions are satisfied, a priori estimates for smooth solutions are obtained. At the end of the paper, there is a discussion on implications of stated results on the well-posedness.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35L80
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 5700557
zbMATH Keywords: energy estimates
zbMATH Keywords: well-posedness
zbMATH Keywords: one space dimension
MaRDI profile type: Publication
full work available at URL: s00208-009-0437-2
OpenAlex ID: W2028276209
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DOI: 10.1007/S00208-009-0437-2
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description: scientific article; zbMATH DE number 5700557