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The aim of this paper is to establish the solvability and global regularitytheory for a new class of generalized anisotropic heat-type boundary valueproblems with (pure) dynamical anisotropic Wentzell boundary conditions. Wefirst prove that the Wentzell operator with the above boundary conditionsgenerates a nonlinear order-preserving submarkovian C_0-semigroup\{T_{\sigma}(t)\} over\mathbb{X\!}^{\,r(\cdot)}(\overline{\Omega}):=L^{r(\cdot)}(\Omega)\timesL^{r(\cdot)}(\Gamma) for all measurable functions r(\cdot) on \overline{\Omega}with 1\leq r^-\leq r^+<\infty. Consequently, the corresponding anisotropicdynamical Wentzell problem is well-posed over\mathbb{X\!}^{\,r(\cdot)}(\overline{\Omega}). Furthermore, we show that thenonlinear C_0-semigroup \{T_{\sigma}(t)\} enjoys a H\"older-typeultracontractivity property in the sense that there exist constantsC_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.

The generalized anisotropic dynamical Wentzell heat equation with nonstandard growth conditions