Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity (Q1181006)

It is established a global existence theorem of nonlinear classical dynamic coupled thermoelasticity for a one-dimensional displacement- temperature initial-boundary value problem with homogeneous boundary conditions. The theorem asserts that for sufficiently ``small'' initial data there is a smooth and unique solution to the problem, and suitably defined norms of the solution vanish or are bounded as the time goes to infinity. The reviewer notes a number of slips and typographical errors, e.g.: 1. The field equations (0.3)-(0.4) are not postulated in a dimensionless form. Therefore, introducing a unit interval \(0<x<1\) as a reference configuration makes a confusion. 2. For the same reason, the definition of the norm: \(| v|_{t,K,L}\) (p. 4) involving the coefficient \((1+s)^ K\), when \(0\leq s\leq t\), and \(t\) is the time, makes another confusion. 3. The hypothesis (4.5), p. 22, in which a constant \(\sigma\) is an upper bound for the three fields of different physical dimensions, can be hardly justified.