  In this work decay estimates are derived for the solutions of 1-D linear
parabolic PDEs with disturbances at both boundaries and distributed
disturbances. The decay estimates are given in the L2 and H1 norms of the
solution and discontinuous disturbances are allowed. Although an eigenfunction
expansion for the solution is exploited for the proof of the decay estimates,
the estimates do not require knowledge of the eigenvalues and the
eigenfunctions of the corresponding Sturm-Liouville operator. Examples show
that the obtained results can be applied for the stability analysis of
parabolic PDEs with nonlocal terms.
