Global existence and formation of singularities in thermoviscoelasticity of integral type∗
Song Jiang, Jaime E. Muñoz Rivera · Applicable Analysis · 2001
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.