## Advances in Differential Equations

### Existence of a solution for a nonlinear system in thermoviscoelasticity

#### Abstract

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

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

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)
MR1785674

Zentralblatt MATH identifier
1002.74027

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

#### Citation

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