Decay rate of solutions to Timoshenko system with past history in unbounded domains
type: Item
instance of: scholarly article
title: Decay rate of solutions to Timoshenko system with past history in unbounded domains
zbMATH Open document ID: 1378.35297
author: Maisa Khader
author: Belkacem Said-Houari
published in: Applied Mathematics and Optimization
publication date: 2017-08-10T00:00:00Z
review text: This paper considers the Cauchy problem for the one-dimensional Timoshenko system which consists of two wave equations describing the transverse vibration of a beam. This is coupled with Gurtin-Pipkin heat conduction for the heat flux. The decay rate of the solutions of this system in thermoelasticity is studied using the energy method in the Fourier space in order to construct an appropriate Lyapunov functional, along with some integral estimates. It is shown that a specific number depending on the parameters of the system which controls the behaviour of the solution in bounded domains, also plays a role in the unbounded situation and affects the decay rate of the solution. A high regularity requirement known as regularity loss is imposed.
reviewed by: Adina Chirila
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 74D05
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 35R09
zbMATH DE Number: 6759146
zbMATH Keywords: energy method
zbMATH Keywords: Lyapunov functional
zbMATH Keywords: Timoshenko system
zbMATH Keywords: Fourier space
zbMATH Keywords: Gurtin-Pipkin heat conduction
zbMATH Keywords: decay rate
zbMATH Keywords: regularity loss
zbMATH Keywords: integral estimates
MaRDI profile type: Publication
full work available at URL: s00245-016-9336-6
OpenAlex ID: W2264915618
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DOI: 10.1007/S00245-016-9336-6
description: scientific article; zbMATH DE number 6759146