GLOBAL SOLVABILITY AND EXPONENTIAL STABILITY IN ONE-DIMENSIONAL NONLINEAR THERMOELASTICITY

We are mainly concerned with the Dirichlet initial boundary value prob lem in one-dimensional nonlinear thermoelasticity. It is proved that i f the initial data are close to the equilibrium then the problem admit s a unique, global, smooth solution. Moreover, as time tends to infini ty, the solution is exponentially stable. As a corollary we also obtai n the existence of periodic solutions for small, periodic right-hand s ides.