The study of partial differential equations (PDE) on spatial domains with physical boundaries supplemented with dynamic boundary conditions (DBC) is closely related to the control of solutions to the models. For example, a given dynamic pressure drop at the physical boundary, associated with a simplified fluid dynamics model, was utilized to control the blood flow through small arteries (Canic 2003). Also, the boundary control problem of the heat equation was studied to find the optimal heat transfer coefficient (Homberg 2013). Comparing with extensive numerical studies, the rigorous analysis of such problems is relatively rare. In this talk, I will present some rigorous mathematical results concerning the stability of large-data solutions to certain nonlinear PDE models, including the 2D Navier-Stokes equations, 2D Boussinesq equations and, if time permits, a system of hyperbolic balance laws from chemotaxis, subject to various types of dynamic boundary conditions.