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.