Global existence of smooth solution to non-linear thermoviscoelastic system with clamped boundary conditions in solid-like materials

In this paper, we prove the global existence and uniqueness of smooth solut ion to a system of one-dimensional non-linear thermoviscoelasticity which d escribes the thermomechanical processes in a class of solid-like materials, such as rubber, etc. The materials satisfy that both ends of the rod are f ixed. This assumption was proposed by Dafermos in 1982 (see [6]). A new app roach is developed to obtain the crucial estimate of the L-infinity-norm of the strain u.