Volume 24, Number 4, October–December 2018
|Page(s)||1511 - 1540|
|Published online||04 December 2018|
Decay estimates for 1-D parabolic PDES with boundary disturbances
Department of Mathematics, National Technical University of Athens, Zografou Campus,
2 Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA
* Corresponding author: firstname.lastname@example.org
Accepted: 18 July 2018
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.
Mathematics Subject Classification: 35K10 / 93D20 / 93C20
Key words: Parabolic partial differential equation / input-to-state stability / non-local PDEs / decay estimates / boundary disturbances
© EDP Sciences, SMAI 2018
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