Spatial asymptotic behaviour in incremental thermoelasticity

Article type: Research Article

Authors: Quintanilla, R.

Affiliations: Matemática Aplicada 2, Universidad Politècnica de Catalunya Colón, 11. Terrassa, Barcelona, Spain Tel.: 34‐937398162, E‐mail: ramon@ma2.upc.es

Abstract: This paper derives spatial decay bounds in a dynamical problem of incremental thermoelasticity defined on a semi‐infinite cylindrical region. Previous results for isothermal elastodynamics and the parabolic heat equation lead us to suspect that the solution of the problem should tend to zero faster than a decaying exponential of the distance from the finite end of the cylinder. We prove that an energy expression is actually bounded above by a decaying exponential of a quadratic polynomial of the distance. As it has been previously proved for usual linear thermoelasticity, this is reminiscent of the decay rate in second order parabolic problems.

Keywords: incremental thermoelastodynamics, spatial estimates, Saint‐Venant's principle

Journal: Asymptotic Analysis, vol. 27, no. 3-4, pp. 265-279, 2001