**Abstract:**
We introduce a class of H-valued parabolic equations on domains, H a Hilbert
space. Coupled boundary conditions of a general form are considered in
dependence of a certain subspace Y of H. This construction has been introduced
by Peter Kuchment: we extend it to the case of time-dependent (so-called
Wentzell-Robin-type) boundary conditions.
This leads to generation of an infinite family of operator semigroups governing
the parabolic equation, one for each Y. Aim of this talk is to show how the
choice of Y affects the properties of the associated semigroup, e.g. by
characterizing its submarkovian property.