Materials with memory: free energies \& solution exponential decay
type: Item
instance of: scholarly article
title: Materials with memory: free energies \& solution exponential decay
zbMATH Open document ID: 1210.80004
author: Sandra Carillo
published in: Communications on Pure and Applied Analysis
publication date: 2010-11-30T00:00:00Z
review text: The temperature evolution within a rigid heat conductor with memory is here considered. Precisely speaking an evolution problem which describes the time evolution of the temperature distribution within a rigid heat conductor with memory is studied. He adopted constitutive equations depending on the history of the material, more precisely speaking the dependence of the heat flux on the history of the temperature gradient is presented by an integral term. Such approach is based on the model proposed by \textit{M. E. Gurtin} and \textit{A. C. Pipkin} [Arch. Ration. Mech. Anal. 31, 113--126 (1968; Zbl 0164.12901)]. So, he considered the evolution problem which is an integro-differential one with assigned initial and boundary condition. The aim of this paper is to prove the exponential decay of solutions to the formulated evolution problem. In the proof the author used the semigroup theory. To show the exponential decay of the solution the author used the free energy functional (so called Graffi-Volterra free energy).
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 74D10
zbMATH DE Number: 5821311
zbMATH Keywords: heat conduction
zbMATH Keywords: free energy
zbMATH Keywords: memory effects
zbMATH Keywords: exponential decay of solutions
reviewed by: Jerzy August Gawinecki
MaRDI profile type: Publication
full work available at URL: cpaa.2010.9.1235
OpenAlex ID: W2032486189
DOI: 10.3934/CPAA.2010.9.1235
description: scientific article; zbMATH DE number 5821311