Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation

Avalos, George; Lasiecka, Irena

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 3, pp. 601-616.

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 ${ℰ}_{min}\left(T\right)$, as terminal time $T\downarrow 0$. Key use is made of the underlying analyticity of the semigroup generated by the elastic operator $𝒜$, as well as of the explicit characterization of its domain of definition. We ultimately find that the blowup rate for ${ℰ}_{min}\left(T\right)$, as $T$ goes to zero, depends on the extent of structural damping.

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