Neumann problem for one-dimensional nonlinear thermoelasticity

Yoshihiro Shibata

Banach Center Publications (1992)

  • Volume: 27, Issue: 2, page 457-480
  • ISSN: 0137-6934

Abstract

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The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.

How to cite

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Shibata, Yoshihiro. "Neumann problem for one-dimensional nonlinear thermoelasticity." Banach Center Publications 27.2 (1992): 457-480. <http://eudml.org/doc/262609>.

@article{Shibata1992,
abstract = {The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.},
author = {Shibata, Yoshihiro},
journal = {Banach Center Publications},
keywords = {classical solutions; Neumann problem; global existence; one-dimensional nonlinear thermoelasticity; nonlinear thermoelasticity; spectral analysis; energy method},
language = {eng},
number = {2},
pages = {457-480},
title = {Neumann problem for one-dimensional nonlinear thermoelasticity},
url = {http://eudml.org/doc/262609},
volume = {27},
year = {1992},
}

TY - JOUR
AU - Shibata, Yoshihiro
TI - Neumann problem for one-dimensional nonlinear thermoelasticity
JO - Banach Center Publications
PY - 1992
VL - 27
IS - 2
SP - 457
EP - 480
AB - The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.
LA - eng
KW - classical solutions; Neumann problem; global existence; one-dimensional nonlinear thermoelasticity; nonlinear thermoelasticity; spectral analysis; energy method
UR - http://eudml.org/doc/262609
ER -

References

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  1. [1] D. E. Carlson, Linear thermoelasticity, in: Handbuch der Physik VIa/2, Springer, Berlin 1977, 297-346. 
  2. [2] B. D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal. 17 (1964), 1-46. 
  3. [3] R. Racke and Y. Shibata, Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity, Arch. Rational Mech. Anal. 116 (1991), 1-34. Zbl0756.73012
  4. [4] M. Slemrod, Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional non-linear thermoelasticity, Arch. Rational Mech. Anal. 76 (1981), 97-133. Zbl0481.73009
  5. [5] Y. Shibata, Local existence theorem in nonlinear thermoelasticity, in preparation. 

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