  We consider existence and uniqueness for several examples of linear parabolic
equations formulated on moving hypersurfaces. Specifically, we study in turn a
surface heat equation, an equation posed on a bulk domain, a novel coupled
bulk-surface system and an equation with a dynamic boundary condition. In order
to prove the well-posedness, we make use of an abstract framework presented in
a recent work by the authors which dealt with the formulation and
well-posedness of linear parabolic equations on arbitrary evolving Hilbert
spaces. Here, after recalling all of the necessary concepts and theorems, we
show that the abstract framework can applied to the case of evolving (or
moving) hypersurfaces, and then we demonstrate the utility of the framework to
the aforementioned problems.
