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This paper provides novel Input-to-State Stability (ISS)-style maximumprinciple estimates for classical solutions of highly nonlinear 1-D parabolicPartial Differential Equations (PDEs). The derivation of the ISS-style maximumprinciple estimates is performed by using an ISS Lyapunov Functional for thesup norm. The estimates provide fading memory ISS estimates in the sup norm ofthe state with respect to distributed and boundary inputs. The obtained resultscan handle parabolic PDEs with nonlinear and non-local in-domain terms/boundaryconditions. Three illustrative examples show the efficiency of the proposedmethodology for the derivation of ISS estimates in the sup norm of the state.

ISS Estimates in the Spatial Sup-Norm for Nonlinear 1-D Parabolic PDEs