Neumann problem for one-dimensional nonlinear thermoelasticity

• Autorzy: Yoshihiro Shibata
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

classical solutions; Neumann problem; global existence; one-dimensional nonlinear thermoelasticity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1992
• Tom: 27
• Numer: 2
• Strony: 457-480

Daty

wydano

1992

Twórcy

autor

Yoshihiro Shibata

• Institute of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki 305, Japan

Bibliografia

• [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.