Advances in Differential Equations

Existence of a solution for a nonlinear system in thermoviscoelasticity

D. Blanchard and O. Guibé

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We prove a few existence results of a solution for a class of nonlinear systems in thermoviscoelasticity in which the mechanical dissipation is not linearized. Under a natural assumption on the growth of the thermal stress with respect to the temperature, we establish an existence result of small solutions. Under a stronger assumption on these stresses for (relative) nonpositive temperature, we prove an existence result for arbitrary data. The techniques of renormalized solutions for a parabolic equation with $L^1$ data are used to handle the energy conservation law.

Article information

Adv. Differential Equations, Volume 5, Number 10-12 (2000), 1221-1252.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 74H20: Existence of solutions
Secondary: 35Q72 74D10: Nonlinear constitutive equations 74F05: Thermal effects


Blanchard, D.; Guibé, O. Existence of a solution for a nonlinear system in thermoviscoelasticity. Adv. Differential Equations 5 (2000), no. 10-12, 1221--1252.

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