Global existence and formation of singularities in thermoviscoelasticity of integral type^∗

^∗Supparted by the SFB 256 of the DFG at the University of Bonn and the GMD-CNPq grant

Abstract

We consider the equations of one-dimensional nonlinear thermoviscoelasticity of integral type. We prove the existence of global smooth solutions to an initial boundary value problem for small initial data in H ²-norm which decay exponentially as time goes to infinity. For a special class of nonlinear thermoviscoelastic materials we prove that if the initial data are large then smooth solutions to the Cauchy problem will develop singularities in finite time.

Keywords:

• Thermoviscoelasticity
• fading memory
• global solution
• blow up

AMS:

• 35K22
• 73B30

^∗Supparted by the SFB 256 of the DFG at the University of Bonn and the GMD-CNPq grant

^∗Supparted by the SFB 256 of the DFG at the University of Bonn and the GMD-CNPq grant

Notes

^∗Supparted by the SFB 256 of the DFG at the University of Bonn and the GMD-CNPq grant