An inverse Stefan problem: identification of boundary value

We propose to determine a function v(t) such that u(O,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 L2(R) by means of a convolution equation. Numerical results are given.