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.
Citation
D. Blanchard. O. Guibé. "Existence of a solution for a nonlinear system in thermoviscoelasticity." Adv. Differential Equations 5 (10-12) 1221 - 1252, 2000. https://doi.org/10.57262/ade/1356651222
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