  For 1-D parabolic PDEs with disturbances at both boundaries and distributed
disturbances we provide ISS estimates in various norms. Due to the lack of an
ISS Lyapunov functional for boundary disturbances, the proof methodology uses
(i) an eigenfunction expansion of the solution, and (ii) a finite-difference
scheme. The ISS estimate for the sup-norm leads to a refinement of the
well-known maximum principle for the heat equation. Finally, the obtained
results are applied to quasi-static thermoelasticity models that involve
nonlocal boundary conditions. Small-gain conditions that guarantee the global
exponential stability of the zero solution for such models are derived.
