  This work studies stability and robustness of a nonlinear system given as an
interconnection of an ODE and a parabolic PDE subjected to external
disturbances entering through the boundary conditions of the parabolic
equation. To this end we develop an approach for a construction of a suitable
coercive Lyapunov function as one of the main results. Based on this Lyapunov
function we establish the well-posedness of the considered system and establish
conditions that guarantee the ISS property. ISS estimates are derived
explicitly for the particular case of globally Lipschitz nonlinearities.
