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We propose to determine a function v(t) such that u(0, t) = v(t), u(x, t) being the temperature in the liquid phase in a medium of water and melting ice. This ill-posed problem is called an inverse Stefan problem. We obtain a regularized solution of this problem with an error estimate in L 2 (R) by means of a convolution equation. Numerical results are given.
MAPMO-URA CNRS No. 1803, Département de Mathématiques et d'Informatique, U.F.R. Faculté des Sciences, Université d'Orléans, BP 675945067 Orléans CedexFrance