Differential and Integral Equations

Stationary solutions to a Strain-gradient type thermoviscoelastic system

Irena Pawłow, Takashi Suzuki, and Sohei Tasaki

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper we study a strain-gradient type thermoviscoelastic system. We focus on the stationary states and their dynamical stability. The adiabatic stationary state is formulated as a nonlinear eigenvalue problem with non-local terms associated with the total energy conservation. One of the purposes of this paper is to extend the results obtained in Suzuki-Tasaki [34]. We reveal a unified structure, called semi-dualities, of the thermoviscoelastic system of viscosity-capillarity type with temperature-dependent viscous and elastic moduli. We describe a physical background and outline the thermodynamic derivation of the system. Based on the semi-dual structure we construct a series of general results concerning the stationary states and their stability. The application of these results together with the bifurcation theory allows us to analyze the total set of the stationary solutions in more detail.

Article information

Source
Differential Integral Equations, Volume 25, Number 3/4 (2012), 289-340.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012737

Mathematical Reviews number (MathSciNet)
MR2917885

Zentralblatt MATH identifier
1265.74012

Subjects
Primary: 74B20: Nonlinear elasticity 74N30: Problems involving hysteresis

Citation

Pawłow, Irena; Suzuki, Takashi; Tasaki, Sohei. Stationary solutions to a Strain-gradient type thermoviscoelastic system. Differential Integral Equations 25 (2012), no. 3/4, 289--340. https://projecteuclid.org/euclid.die/1356012737


Export citation