Time-asymptotic stability of non-newtonian fluid or plastic solid

We consider adiabatic shearing of solids exhibiting strain rate sensitivity and thermal softening or non-Newtonian liquids with temperature dependent viscosity. The processes are caused by a steady boundary force. We prove that there exists a unique solution and, as the time tends to ∞, the processes converge to the shearing under constant shear stress. The proof is based on a priori estimates, which are obtained with the help of identities for solutions of the system of conservation laws and constitutive relation describing the processes. The result idicates that, as expected, the viscosity or thermal diffusion play a stabilizing role.