Bl. Guo et Pc. Zhu, Global existence of smooth solution to non-linear thermoviscoelastic system with clamped boundary conditions in solid-like materials, COMM MATH P, 203(2), 1999, pp. 365-383
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.