Global solutions to the equation of thermoelasticity with fading memory

Mari Okada; Shuichi Kawashima

doi:10.1016/j.jde.2017.02.037

Global solutions to the equation of thermoelasticity with fading memory

Mari Okada^*, Shuichi Kawashima

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (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 language	English
Pages (from-to)	338-364
Number of pages	27
Journal	Journal of Differential Equations
Volume	263
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2017.02.037
Publication status	Published - 2017 Jul 5
Externally published	Yes

Keywords

Asymptotic stability
Global existence
Thermoelasticity with memory

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2017.02.037

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title = "Global solutions to the equation of thermoelasticity with fading memory",

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.",

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author = "Mari Okada and Shuichi Kawashima",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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AU - Okada, Mari

AU - Kawashima, Shuichi

PY - 2017/7/5

Y1 - 2017/7/5

N2 - 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.

AB - 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.

KW - Asymptotic stability

KW - Global existence

KW - Thermoelasticity with memory

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ER -

Global solutions to the equation of thermoelasticity with fading memory

Abstract

Keywords

ASJC Scopus subject areas

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