  This paper presents a maximum principle-based approach in the establishment
of input-to-state stability (ISS) for a class of nonlinear parabolic partial
differential equations (PDEs) over higher dimensional domains with variable
coefficients and different types of nonlinear boundary conditions. Technical
development on ISS analysis of the considered systems is detailed, and an
example of establishing ISS estimates for a nonlinear parabolic equation with,
respectively, a nonlinear Robin boundary condition and a nonlinear Dirichlet
boundary condition is provided to illustrate the application of the developed
method.
