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Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity. (English) Zbl 0756.73012
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.

##### MSC:
 74A15 Thermodynamics in solid mechanics 74B20 Nonlinear elasticity 35Q72 Other PDE from mechanics (MSC2000)
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##### References:
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