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


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 Emin (T), as terminal time T ↓ 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 Emin (T), as T goes to zero, depends on the extent of structural damping.

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Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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