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

• George Avalos ^[2] ; Irena Lasiecka ^[1]
  1. [1] University of Virginia

     University of Virginia

     Estados Unidos

     
  2. [2] University of Nebraska-Linciln
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 2, Nº 3, 2003, págs. 601-616
• Idioma: inglés
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• Resumen

  • 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 }(T), 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 }(T), as T goes to zero, depends on the extent of structural damping.