  We consider parabolic systems with nonlinear dynamic boundary conditions, for
which we give a rigorous derivation. Then, we give them several physical
interpretations which includes an interpretation for the porous-medium
equation, and for certain reaction-diffusion systems that occur in mathematical
biology and ecology. We devise several strategies which imply (uniform)}$L^{p}
and}$L^{\infty}$ estimates on the solutions for the initial value problems
considered.
