Uniqueness and spatial stability are investigated for smooth solutions to boundary value
problems in non-classical linearised and linear thermoelasticity subject to certain conditions
on material coefficients. Uniqueness is derived for standard boundary conditions
on bounded regions using a generalisation of Kirchhoff’s method. Spatial stability is discussed
for the semi-infinite prismatic cylinder in the absence of specified axial asymptotic
behaviour. Alternative growth and decay estimates are established principally for the
cross-sectional energy flux that is shown to satisfy a first order differential inequality.
Uniqueness in the class of solutions with bounded energy follows as a corollary.
Separate discussion is required for the linearised and linear theories. Although the general
approach is similar for both theories, the argument must be considerably modified for
the treatment of the linear theory.
Fernández-Sare, H.; Muñoz , J.; Quintanilla, R. International journal of engineering science Vol. 48, num. 11, p. 1233-1241 DOI: 10.1016/j.ijengsci.2010.04.014 Data de publicació: 2010-11-01 Article en revista
In this paper we investigate the asymptotic behavior of the semigroup associated to the solutions of the initial boundary value problem for a one-dimensional nonsimple thermoelastic solids. We show that the semigroup is exponentially stable but is not analytic. Moreover we show the impossibility of time localization of the solutions.
Continuous dependence on the initial time geometry is established for the mean-square
integral of the displacement in a linear inhomogeneous anisotropic elastic semi-infinite
cylinder in motion subject to a prescribed time-dependent base displacement and initial
data. A bound, newly derived for the total energy, in conjunction with backward continuation
in time of the unperturbed and perturbed displacements, is employed to obtain the