  The original KWC-system is widely used in materials science. It was proposed
in [Kobayashi et al, Physica D, 140, 141--150 (2000)] and is based on the phase
field model of planar grain boundary motion. This model suffers from two key
challenges. Firstly, it is difficult to establish its relation to physics, in
particular, a variational model. Secondly, it lacks uniqueness. The former has
been recently studied within the realm of BV-theory. The latter only holds
under various simplifications. This article introduces a pseudo-parabolic
version of the KWC-system. A direct relationship with variational model (as
gradient-flow) and uniqueness are established without making any unrealistic
simplifications. Namely, this is the first KWC-system which is both physically
and mathematically valid. The proposed model overcomes the well-known open
issues.
