Improved spatial decay bounds in generalized heat conduction

Abstract

This paper deals with heat conduction in a semi-infinite cylinder using the generalized Maxwell-Cattaneo equations. Spatial decay bounds for the temperature and heat flux under two different types of boundary conditions are derived. For fixed time it is shown that in each case the solutions decay in appropriate measure like the exponential of a quadratic function of the distance from the base of the cylinder, whereas in previous work they had been shown to decay only at least as fast as the exponential of a linear function.