Geodesic
Decay estimates for 1-D parabolic PDES with boundary disturbances
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1511-1540

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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.

DOI : 10.1051/cocv/2018043
Classification : 35K10, 93D20, 93C20
Keywords: Parabolic partial differential equation, input-to-state stability, non-local PDEs, decay estimates, boundary disturbances

Karafyllis, Iasson 1 ; Krstic, Miroslav 1

1 
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     title = {Decay estimates for {1-D} parabolic {PDES} with boundary disturbances},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1511--1540},
     publisher = {EDP-Sciences},
     volume = {24},
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     year = {2018},
     doi = {10.1051/cocv/2018043},
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Karafyllis, Iasson; Krstic, Miroslav. Decay estimates for 1-D parabolic PDES with boundary disturbances. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1511-1540. doi: 10.1051/cocv/2018043

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