Differential and Integral Equations

Stationary solutions to a Strain-gradient type thermoviscoelastic system

Irena Pawłow, Takashi Suzuki, and Sohei Tasaki

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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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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