On the temperature distribution in cold ice (Q1267762)

Summary: A linear heat equation predicts that the variations of temperature along a cold ice sheet (i.e. at a temperature less than is freezing point) due to a sudden increase in air temperature, are very very slow. Based on this we represent the nonlinear evolution of an ice sheet as a sequence of steady states. As a first fundamental indication that this model is correct, well posedness with respect to the variations of initial and boundary data is proved. Further an estimate of the error made in evaluating the thickness is given.