  The aim of this paper is to establish the solvability and global regularity
theory for a new class of generalized anisotropic heat-type boundary value
problems with (pure) dynamical anisotropic Wentzell boundary conditions. We
first prove that the Wentzell operator with the above boundary conditions
generates a nonlinear order-preserving submarkovian C_0-semigroup
\{T_{\sigma}(t)\} over
\mathbb{X\!}^{\,r(\cdot)}(\overline{\Omega}):=L^{r(\cdot)}(\Omega)\times
L^{r(\cdot)}(\Gamma) for all measurable functions r(\cdot) on \overline{\Omega}
with 1\leq r^-\leq r^+<\infty. Consequently, the corresponding anisotropic
dynamical Wentzell problem is well-posed over
\mathbb{X\!}^{\,r(\cdot)}(\overline{\Omega}). Furthermore, we show that the
nonlinear C_0-semigroup \{T_{\sigma}(t)\} enjoys a H\"older-type
ultracontractivity property in the sense that there exist constants
C_1,\,C_2,\,\kappa>0, and \gamma\in(0,1), such that
|\|T_{\sigma}(t)\mathbf{u}_0-T_{\sigma}(t)\mathbf{v}_0\||_{_{\infty}}\,\leq\,
C_1\,e^{C_2t}t^{-\kappa}|\|\mathbf{u}_0-\mathbf{v}_0\||^{\gamma}_{_{r(\cdot),s(\cdot)}}
for every
\mathbf{u}_0,\,\mathbf{v}_0\in\mathbb{X\!}^{\,r(\cdot),s(\cdot)}(\overline{\Omega})
and for all t>0.
