Advances in Differential Equations
- Adv. Differential Equations
- Volume 5, Number 10-12 (2000), 1221-1252.
Existence of a solution for a nonlinear system in thermoviscoelasticity
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.
Adv. Differential Equations Volume 5, Number 10-12 (2000), 1221-1252.
First available in Project Euclid: 27 December 2012
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Blanchard, D.; Guibé, O. Existence of a solution for a nonlinear system in thermoviscoelasticity. Adv. Differential Equations 5 (2000), no. 10-12, 1221--1252. https://projecteuclid.org/euclid.ade/1356651222