The existence and uniqueness of weak solutions of dynamical low-rank evolution for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.

中文翻译：

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抛物线问题的动态低秩逼近的存在

展示了二维抛物线偏微分方程动态低阶演化弱解的存在唯一性，也包括椭圆部分的非对角扩散。该证明基于低秩流形上的变分时间步长方案。此外，该方案被证明与计算这种低秩演化的实际方法密切相关。