This article is a continuation of an earlier work (Huang and Ye in Int Math Res Not, 2017. https://doi.org/10.1093/imrn/rnx278), where the long time existence and convergence for some special cases of parabolic type special Lagrangian equations were given. The long time existence and convergence of the flow are obtained for all cases in this article. In particular, we can prescribe the second boundary value problems for a family of special Lagrangian graphs.

中文翻译：

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关于一类完全非线性流的第二边值问题 I

本文是早期工作的延续（Huang and Ye in Int Math Res Not, 2017. https://doi.org/10.1093/imrn/rnx278），其中抛物型的一些特殊情况的长期存在和收敛给出了特殊的拉格朗日方程。本文得到了所有情况下流的长时间存在和收敛。特别地，我们可以为一族特殊的拉格朗日图规定第二个边值问题。