Conditional stability up to the final time for backward-parabolic equations with Log-Lipschitz coefficients

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, Jaeh and Prizzi (2015), concerning conditional stability (of a type intermediate between Hoelder and logarithmic), arbitrarily closed, but not up to the final time.