The null controllability problem for a structurally damped abstract wave equation -often referred to in the literature as a structurally damped equation- is considered with a view towards obtaining optimal rates of blowup for the associated minimal energy function ${\mathcal{E}}_{min}\left(T\right)$, as terminal time $T\downarrow 0$. Key use is made of the underlying analyticity of the semigroup generated by the elastic operator $\mathcal{A}$, as well as of the explicit characterization of its domain of definition. We ultimately find that the blowup rate for ${\mathcal{E}}_{min}\left(T\right)$, as $T$ goes to zero, depends on the extent of structural damping.

@article{ASNSP_2003_5_2_3_601_0, author = {Avalos, George and Lasiecka, Irena}, title = {Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {601--616}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 2}, number = {3}, year = {2003}, mrnumber = {2020861}, zbl = {1170.35470}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2003_5_2_3_601_0/} }

TY - JOUR AU - Avalos, George AU - Lasiecka, Irena TI - Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 601 EP - 616 VL - 2 IS - 3 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2003_5_2_3_601_0/ LA - en ID - ASNSP_2003_5_2_3_601_0 ER -

%0 Journal Article %A Avalos, George %A Lasiecka, Irena %T Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 601-616 %V 2 %N 3 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_2003_5_2_3_601_0/ %G en %F ASNSP_2003_5_2_3_601_0

Avalos, George; Lasiecka, Irena. Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 2 (2003) no. 3, pp. 601-616. http://www.numdam.org/item/ASNSP_2003_5_2_3_601_0/

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