Some inverse problems for a nonlinear parabolic equation connected with continuous casting of steel: Stability estimates and regularization∗

We consider a nonlinear parabolic equation which models the secondary cooling of steel in continuous slab casting and provide quantitative stability results both for the problem of determining the solidification front from measured Cauchy data and for the inverse problem of determining a cooling strategy that leads to a prescribed solidification front. For the latter problem, also stability and convergence of Tikhonov regularization are proved. ∗Supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, projects S32/03 and P7869-PHY and by M.P.I. ∗Supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, projects S32/03 and P7869-PHY and by M.P.I. Notes ∗Supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, projects S32/03 and P7869-PHY and by M.P.I.