Existence of dynamical low-rank approximations to parabolic problems

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.

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