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

George Avalos; Irena Lasiecka

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2003)

  • Volume: 2, Issue: 3, page 601-616
  • ISSN: 0391-173X

Abstract

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

How to cite

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Avalos, George, and 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 2.3 (2003): 601-616. <http://eudml.org/doc/84513>.

@article{Avalos2003,
abstract = {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.},
author = {Avalos, George, Lasiecka, Irena},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {601-616},
publisher = {Scuola normale superiore},
title = {Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation},
url = {http://eudml.org/doc/84513},
volume = {2},
year = {2003},
}

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
PB - Scuola normale superiore
VL - 2
IS - 3
SP - 601
EP - 616
AB - 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.
LA - eng
UR - http://eudml.org/doc/84513
ER -

References

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