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March/April 2012 Stationary solutions to a Strain-gradient type thermoviscoelastic system
Irena Pawłow, Takashi Suzuki, Sohei Tasaki
Differential Integral Equations 25(3/4): 289-340 (March/April 2012). DOI: 10.57262/die/1356012737


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.


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Irena Pawłow. Takashi Suzuki. Sohei Tasaki. "Stationary solutions to a Strain-gradient type thermoviscoelastic system." Differential Integral Equations 25 (3/4) 289 - 340, March/April 2012.


Published: March/April 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1265.74012
MathSciNet: MR2917885
Digital Object Identifier: 10.57262/die/1356012737

Primary: 74B20 , 74N30

Rights: Copyright © 2012 Khayyam Publishing, Inc.

Vol.25 • No. 3/4 • March/April 2012
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