A solution technique for random and nonlinear inverse heat conduction problems

Some inverse problems for the nonlinear heat equation are considered in this paper. They consist in the statistical evaluation of certain temperature properties of a conducting body or heat source functions, in the assumption that the temperature registered at an interior point is known as a random function of the time. The proposed approach is based on suitable partitions of the one-dimensional space domain, and on piecewise cubic spline approximations of the sample functions to be determined. Quantitative results on the mean, variance and probability densities joined to the unknown random functions are deduced in some pertinent applications.