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A new maximality argument for a coupled fluid-structure interaction, with implications for a divergence-free finite element method

George AvalosMatthew Dvorak — 2008

Applicationes Mathematicae

We consider a coupled PDE model of various fluid-structure interactions seen in nature. It has recently been shown by the authors [Contemp. Math. 440, 2007] that this model admits of an explicit semigroup generator representation 𝓐:D(𝓐)⊂ H → H, where H is the associated space of fluid-structure initial data. However, the argument for the maximality criterion was indirect, and did not provide for an explicit solution Φ ∈ D(𝓐) of the equation (λI-𝓐)Φ =F for given F ∈ H and λ > 0. The present...

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

George AvalosIrena Lasiecka — 2003

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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 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...

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