An inverse problem for a system with a moving boundary (Q1375644)

The paper treats the inverse Stefan problem for an initial-boundary value problem for a nonlinear parabolic equation in a plane polygonal domain, i.e. finding the right-hand side of the equation given (inexact) observations of the solution at sufficiently frequent time instants. The approach to the solution of the problem relies on ideas in the theory of games [see \textit{N. N. Krasovskij} and \textit{A. I. Subbotin}, Positional differential games (1974; Zbl 0298.90067)], it uses a technique due to \textit{C. M. Elliot} [IMA J. Numer. Anal. 7, 61-71 (1987; Zbl 0638.65088)]. After partition of the time interval a finite element algorithm is constructed at the discrete time levels. The procedure converges in the \(L_2\)-norm, it is stable with respect to informational noise and computational errors.