End effects in thermoelasticity
Ramón Quintanilla · Mathematical Methods in the Applied Sciences · 2001
This paper derives spatial decay bounds in a dynamical problem of 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 thermoelastic 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. This is reminiscent of the decay rate in the second-order parabolic problems. Similar arguments are sketched for the case of a non-prismatic cylinder, and a non-linear heat conduction problem for a rigid body is considered. Some extensions and generalizations are indicated in the final section. Copyright © 2001 John Wiley & Sons, Ltd.