In this paper we study the backward uniqueness for parabolic equations with non-Lipschitz coefficients in time and space. The result presented here improves an old uniqueness theorem due to Lions and Malgrange  and some more recent results of Del Santo and Prizzi [5, 6].
"Backward uniqueness for parabolic operators with non-Lipschitz coefficients." Osaka J. Math. 52 (3) 793 - 817, July 2015.