Convergence Results for Generalized Heat Conduction as the Relaxation Time Tends to Zero Original Research Article

Using heat conduction equations that have been proposed for low temperature, this paper studies the convergence of the solution as the relaxation time τ tends to zero. It is first shown that in energy norm the convergence rate is at least O(τ). For a time integrated measure the convergence rate is seen to be O(τ). In each case explicit bounds in terms of data are obtained.