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 L^{2} and H^{1} 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.
Keywords: Parabolic partial differential equation, input-to-state stability, non-local PDEs, decay estimates, boundary disturbances
@article{COCV_2018__24_4_1511_0, author = {Karafyllis, Iasson and Krstic, Miroslav}, 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}, number = {4}, year = {2018}, doi = {10.1051/cocv/2018043}, mrnumber = {3922445}, zbl = {1412.35159}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2018043/} }
TY - JOUR AU - Karafyllis, Iasson AU - Krstic, Miroslav TI - Decay estimates for 1-D parabolic PDES with boundary disturbances JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1511 EP - 1540 VL - 24 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2018043/ DO - 10.1051/cocv/2018043 LA - en ID - COCV_2018__24_4_1511_0 ER -
%0 Journal Article %A Karafyllis, Iasson %A Krstic, Miroslav %T Decay estimates for 1-D parabolic PDES with boundary disturbances %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1511-1540 %V 24 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2018043/ %R 10.1051/cocv/2018043 %G en %F COCV_2018__24_4_1511_0
Karafyllis, Iasson; Krstic, Miroslav. Decay estimates for 1-D parabolic PDES with boundary disturbances. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 4, pp. 1511-1540. doi : 10.1051/cocv/2018043. http://archive.numdam.org/articles/10.1051/cocv/2018043/
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