An inverse Stefan problem: Identification of boundary value
A spatially one-dimensional inverse Stefan problem is considered: the moving boundary (its evolution in time) is given, the temporal evolution of the temperature at the non-moving boundary is to be determined. The standard integral equation of first kind for this problem is transformed into an equivalent convolution equation. Under the assumption that the data function is perturbed by (small) errors a regularized solution is constructed via Fourier transform and an \(L^2\) error bound is found. Then a numerical case study is documented.
scientific article; zbMATH DE number 908311