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Decay estimates for 1-D parabolic PDEs with boundary disturbances. (English) Zbl 1412.35159

In the work, decay estimates are derived for the solution of 1-D linear parabolic PDEs with disturbances at both boundaries and distributed disturbances. The structure of the paper is as follows. First, in Sections 2 and 3, the authors give the problem statement and formulate the main results of the paper. The applications of the obtained decay estimates to the stability analysis of parabolic PDEs with nonlocal terms are illustrated in Section 4. Section 5 contains the proofs of all results. A brief conclusion is given in Section 6.

MSC:

35K10 Second-order parabolic equations
93D20 Asymptotic stability in control theory
93C20 Control/observation systems governed by partial differential equations
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