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ArticleOriginal scientific text

Title

Neumann problem for one-dimensional nonlinear thermoelasticity

Authors 1

Affiliations

  1. Institute of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki 305, Japan

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.

Keywords

ENG
classical solutions, Neumann problem, global existence, one-dimensional nonlinear thermoelasticity

Bibliography

  1. D. E. Carlson, Linear thermoelasticity, in: Handbuch der Physik VIa/2, Springer, Berlin 1977, 297-346.
  2. B. D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal. 17 (1964), 1-46.
  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.
  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.
  5. Y. Shibata, Local existence theorem in nonlinear thermoelasticity, in preparation.
Banach Center Publications
1992/27/2
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Pages:
457-480
Main language of publication
English
Published
1992
Exact and natural sciences