A smoothing spline-based method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model in two-dimensions. An ill-posed inverse problem involving recovery of the initial temperature distribution from measurements of the final temperature distribution is investigated. A hyperbolic heat conduction model is considered instead of a parabolic model and smoothing splines are applied to regularize the recovered initial profile. The comparison of the proposed procedure and parabolic model is presented graphically by examples.
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