The existence and uniqueness of weak solutions to dynamical low-rank evolution problems 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.

翻译：在两个空间层面,抛物线部分差异方程式的动态低级进化问题解决方案存在薄弱,其独特性和独特性也得到了证明,其中也包括了椭圆部分的非对角扩散。证据基于对低级方块的变换时间步骤计划。此外,这一计划与计算这种低级进化的实用方法密切相关。