Spatial decay estimates for the Maxwell-Cattaneo equations with mixed boundary conditions (Q1764404)

The Maxwell-Cattaneo equations governing the evolution of heat flux \(\Phi\) and temperature \(T\) feature a specific model for heat conduction accounting for finite propagation speed. In the framework of this model the propagation of heat in a cylindrical domain \(R\;:=D\times\mathbb{R}_{>0}\) is considered in the absence of volume heat sources and vanishing initial data but with inhomogeneous boundary conditions \(n\times\Phi=F,\; T=G\) on \(\partial R\), where \(F\), \(G\) are assumed to be supported only on the `bottom part' \(D\times\left\{ 0\right\} \) of \(\partial R\). The authors present decay estimates showing exponential decay of temperature and heat flux in terms of certain energy quantities in the infinite space direction \(\left(0,0,1\right)\) of the semi-infinite cylinder \(R\).