Prof. David Iron


UC Irvine


Monday, November 17, 2003 - 4:00pm


MSTB 254

We consider two different classes of models which arise from the study of microwave heating of ceramics in a single-mode resonant cavity. The stability and dynamics of hot-spot solutions to the two classes of scalar, nonlocal, singularly perturbed reaction-diffusion equations are analyzed. For the first model, where the coefficients in the differential operator are spatially homogeneous, an explicit characterization of metastable(exponetially slow motion) hot-spot behaviour is given in the limit of small thermal diffusivity. For the second model, where the differential operator has a spatially inhomogeneous term resulting from the variation in the electric field along the ceramic sample, a hot-spot solution is shown to propagate on an algebraically long time-scale towards the point of maximum field strength.