Local well-posedness for the nonlinear heat and Schr\"{o}dinger equations with nonlinear Wentzell boundary conditions on time-dependent compact Riemannian manifolds

We prove a local well-posedness result for the semilinear heat and Schr\"{o}dinger equations with subcritical nonlinearities posed on a time-dependent compact Riemannian manifold and supplied with a nonlinear dynamical boundary condition of Wentzell type.