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

Authors: Andreas Binder, Heinz W. Engl, and S. Vesella

Abstract: 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.