The present paper is devoted to the study of the existence, the uniqueness and the stability of transition fronts of non-local dispersal equations in time heterogeneous media of bistable type under the unbalanced condition. We first study space non-increasing transition fronts and prove various important qualitative properties, including uniform steepness, stability, uniform stability and exponential decaying estimates. Then, we show that any transition front, after certain space shift, coincides with a space non-increasing transition front (if it exists), which implies the uniqueness, up-to-space shifts and monotonicity of transition fronts provided that a space non-increasing transition front exists. Moreover, we show that a transition front must be a periodic travelling front in periodic media and asymptotic speeds of transition fronts exist in uniquely ergodic media. Finally, we prove the existence of space non-increasing transition fronts, whose proof does not need the unbalanced condition.

中文翻译：

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时间异质双稳态介质中非局部方程跃迁前沿的存在性、唯一性和稳定性

本文致力于研究不平衡条件下双稳态时间非均质介质中非局域色散方程的存在性、唯一性和过渡前沿的稳定性。我们首先研究空间非增加过渡前沿并证明各种重要的定性性质，包括均匀陡度、稳定性、均匀稳定性和指数衰减估计。然后，我们证明任何过渡前沿，在一定的空间位移之后，都与空间非增加过渡前沿（如果存在）重合，这意味着过渡前沿的唯一性，向上空间位移和单调性，前提是空间非-存在增加的过渡前沿。而且，我们表明，过渡前沿必须是周期性媒体中的周期性行进前沿，并且过渡前沿的渐近速度存在于唯一遍历媒体中。最后，我们证明了空间非增过渡前沿的存在，其证明不需要不平衡条件。