On existence and uniqueness in incremental thermoelasticity (Q800115)

Existence, continuous data dependence and uniqueness are proved for solutions to the standard initial boundary value problem in the theory of small thermoelastic deformations superposed upon a large time-dependent displacement and temperature [\textit{D. Iesan}, Incremental equations in thermoelasticity, J. Therm. Stresses 3, 41-56 (1980)]. Previous discussion has been restricted to large uniform deformation and temperature [e.g. \textit{A. H. England} and \textit{A. E. Green}, Philos. Trans. R. Soc. Lond., A 253, 517-542 (1961)]. The problem is converted into an abstract nonhomogeneous evolutionary equation on a Hilbert space and the results are obtained by means of semigroup theory.