Thermal blow-up in a subdiffsive medium with a localized energy source is examined for a spatial domain of infinite extent in one, two, and three dimensions. An analysis of a nonlinear model of this problem reveals that a blow-up always occurs, independent of the spatial dimension and the thermal properties of the material. This behavior is in contrast with both classical diffusion and superdiffusion, where the prevention of a blow-up depends upon spatial dimension as well as the thermal properties of the medium. The asymptotic growth of the temperature near blow-up is determined for energy sources whose output increases in either an algebraic or exponential manner.
|Journal||Fractional Calculus and Applied Analysis|
|State||Published - 2009|