We prove continuous dependence on initial data for a backward parabolic operator whose leading coefficients are Osgood continuous in time. This result fills the gap between uniqueness and continuity results obtained so far.

中文翻译：

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具有Osgood连续系数的后向抛物线算子的条件稳定性

我们证明了前导系数在时间上连续为Osgood的后向抛物线算子对初始数据的持续依赖。该结果填补了迄今为止获得的唯一性和连续性结果之间的空白。