Identification of a boundary influx condition in a one-phase Stefan problem

英文摘要：

We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a logarithmic stability estimate that shows that the inversion is ill-posed. The proof is based on integral equations and unique continuation for holomorphic functions. We also proposed a direct algorithm with a regularization term to solve the nonlinear inverse problem. Several numerical tests using noisy data are provided with relative errors analysis.