The Influence of Domain and Diffusivity Perturbations on the Decay of End Effects in Heat Conduction
Changhao Lin, Lawrence Edward Payne · SIAM Journal on Mathematical Analysis · 1994
For a standard heat conduction problem in a semi-infinite cylinder the authors investigate the influence of domain perturbation and of the variation of the diffusivity coefficient on the decay of Saint Venant end effects. The particular problem investigated is one in which the lateral surface of the cylinder is maintained at zero temperature and a nonzero temperature is prescribed on the near end. Energy methods are used to assess the influence of the perturbations. A Phragmén–Lindelöf type alternative and explicit decay bounds are derived.