Global solutions to the equation of thermoelasticity with fading memory

Mari Okada, Shuichi Kawashima

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider the initial-history value problem for the one-dimensional equation of thermoelasticity with fading memory. It is proved that if the data are smooth and small, then a unique smooth solution exists globally in time and converges to the constant equilibrium state as time goes to infinity. Our proof is based on a technical energy method which makes use of the strict convexity of the entropy function and the properties of strongly positive definite kernels.

Original languageEnglish
Pages (from-to)338-364
Number of pages27
JournalJournal of Differential Equations
Volume263
Issue number1
DOIs
Publication statusPublished - Jul 5 2017

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Fading Memory
Thermoelasticity
Equilibrium constants
Global Solution
Entropy
Positive Definite Kernels
Strict Convexity
Data storage equipment
Entropy Function
Energy Method
Smooth Solution
Equilibrium State
Infinity
Converge
History

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Global solutions to the equation of thermoelasticity with fading memory. / Okada, Mari; Kawashima, Shuichi.

In: Journal of Differential Equations, Vol. 263, No. 1, 05.07.2017, p. 338-364.

Research output: Contribution to journalArticle

Okada, Mari ; Kawashima, Shuichi. / Global solutions to the equation of thermoelasticity with fading memory. In: Journal of Differential Equations. 2017 ; Vol. 263, No. 1. pp. 338-364.
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