Abstract
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 may be severely ill-posed. The proof is based on integral equations and unique continuation of 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.
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