Existence of dynamical low-rank approximations to parabolic problems

Markus Bachmayr, Henrik Eisenmann, Emil Kieri, and André Uschmajew

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Submission date: 27. Feb. 2020 (revised version: December 2020)
Pages: 31
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Abstract:
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.