Numerical and asymptotic analysis of a localized heat source undergoing periodic motion Original Research Article

A highly localized heat source moves with simple periodic motion along a one-dimensional medium with reactive-diffusive properties. It is known that the system will experience a blow-up in finite time. Numerical results suggest that this blow-up, though unavoidable, can be delayed by increasing either the amplitude or the frequency of the motion. These numerical results are compared to known analytical results. Numerical and analytical results are also compared for the related case in which the heat source moves at a constant speed in one direction. The asymptotic behavior of the temperature of the material at the location of the heat source near the time of blow-up is also analyzed. It can be of interest to consider the asymptotic behavior of the solution in the context of the numerical solution in order to gain confidence in the numerical results.