601	RWTH Publication No: 960329        2020
TITLE	Existence of dynamical low-rank approximations to parabolic problems
AUTHORS	Markus Bachmayr, Henrik Eisenmann, Emil Kieri, André Uschmajew
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.
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