We prove logarithmic conditional stability up to the final time for backward-parabolic operators whose coefficients are Log-Lipschitz continuous in t and Lipschitz continuous in x. The result complements previous achievements of Del Santo and Prizzi (2009) and Del Santo, Jäh and Prizzi (2015), concerning conditional stability (of a type intermediate between Hölder and logarithmic), arbitrarily closed, but not up to the final time.
