Optimal decay rate of the energy for wave equations with critical potential
type: Item
instance of: scholarly article
title: Optimal decay rate of the energy for wave equations with critical potential
zbMATH Open document ID: 1267.35034
author: Ryo Ikehata
author: Grozdena Todorova
author: Borislav Yordanov
published in: Journal of the Mathematical Society of Japan
publication date: 2013-04-09T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jmsj/1359036453
review text: The authors study the long time behaviour of the solutions of the wave equation with a variable damping term. They are focused to the Cauchy problem for the case of potentials with critical decay. Their solution manifests a new threshold effect with respect to the size of the coefficient in the variable damping term. In additon, they obtain similar results in low dimensions and they have presented the estimates in the two dimensional case. Moreover, they determined that the decay estimate of the associated parabolic problem when the size of the coefficient in the variable damping term is much larger than 3.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 6152432
zbMATH Keywords: wave equations
zbMATH Keywords: critical potential
zbMATH Keywords: optimal decay rate
zbMATH Keywords: variable damping term
zbMATH Keywords: new threshold effect
reviewed by: Ömer Kavaklioglu
MaRDI profile type: Publication
OpenAlex ID: W1971804477
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DOI: 10.2969/JMSJ/06510183
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description: scientific article; zbMATH DE number 6152432