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Journal of Evolution Equations

, Volume 9, Issue 2, pp 341–370 | Cite as

Boundary feedback stabilization of a coupled parabolic–hyperbolic Stokes–Lamé PDE system

  • George Avalos
  • Roberto TriggianiEmail author
Article

Abstract

We consider a parabolic–hyperbolic coupled system of two partial differential equations (PDEs), which governs fluid–structure interactions, and which features a suitable boundary dissipation term at the interface between the two media. The coupled system consists of Stokes flow coupled to the Lamé system of dynamic elasticity, with the respective dynamics being coupled on a boundary interface, where dissipation is introduced. Such a system is semigroup well-posed on the natural finite energy space (Avalos and Triggiani in Discr Contin Dynam Sys, to appear). Here we prove that, moreover, such semigroup is uniformly (exponentially) stable in the corresponding operator norm, with no geometrical conditions imposed on the boundary interface. This result complements the strong stability properties of the undamped case (Avalos and Triggiani in Discr Contin Dynam Sys, to appear).

Mathematics Subject Classification (2000)

Primary 35Q30 Secondary 73C02 73K12 76D07 93 

Keywords

Fluid–structure interaction Uniform stabilization 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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