Convergence results for generalized heat condution as the relaxation time tends to zero (Q5937655)

The behaviour of a system for heat conduction at low temperature, relating heat flux and temperature is being studied. More particularly, the convergence of the solution of the system is examined as the relaxation time \(\tau\) tends to zero. In Section 2 it is proved that the solution of the system converges in energy norm to the solution of a related initial-boundary value problem as \(\tau\rightarrow 0\) at least at a rate of \(O(\sqrt{\tau})\). NEWLINENEWLINENEWLINEIn the next section a significant improvement of the rate of convergence is presented by employing a time-integrated measure. Finally, it is noted that the results of the derivation of convergence estimates can be extended for nonstar-shaped regions.