ISS-like estimates for nonlinear parabolic PDEs with variable coefficients on higher dimensional domains

Abstract This paper presents a maximum principle-based approach in the establishment of ISS-like estimates for a class of nonlinear parabolic partial differential equations (PDEs) with variable coefficients and different types of nonlinear boundary conditions on higher dimensional domains. Comparing with the existing literature, the ISS-like estimates established in this paper are independent of the nonlinear terms of the PDEs. Technical development on ISS analysis of the considered systems is detailed, and an example of establishing ISS-like 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.