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2001 | 11 | 6 | 1231-1248

Tytuł artykułu

Exact controllability of an elastic membrane coupled with a potential fluid

Autorzy

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
We consider the problem of boundary control of an elastic system with coupling to a potential equation. The potential equation represents the linearized motions of an incompressible inviscid fluid in a cavity bounded in part by an elastic membrane. Sufficient control is placed on a portion of the elastic membrane to insure that the uncoupled membrane is exactly controllable. The main result is that if the density of the fluid is sufficiently small, then the coupled system is exactly controllable.

Rocznik

Tom

11

Numer

6

Strony

1231-1248

Opis fizyczny

Daty

wydano
2001

Twórcy

autor
  • Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A.

Bibliografia

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  • Banks H.T., Silcox R.J. and Smith R.C. (1993): The modeling and control of acoustic/structure interaction problems via peizoceramic actuators: 2-d numerical examples. — ASME J. Vibr. Acoust., Vol.2, pp.343–390.
  • Bardos C., Lebeau G. and Rauch J. (1992): Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. — SIAM J. Contr., Vol.30, No.5, pp.1024–1065.
  • Conca C., Osses A. and Planchard J. (1998): Asympotic analysis relating spectral models in fluid-solid vibrations. — SIAM J. Num. Anal., Vol.35, No.3, pp.1020–1048.
  • Galdi G.D., (1994): An Introduction to the Mathematical Theory of Navier-Stokes Equations, Vol.I. — New York: Springer.
  • Hansen S.W. and Lyashenko A. (1997): Exact controllability of a beam in an incompressible inviscid fluid. — Disc. Cont. Dyn. Syst., Vol.3., No.1, pp.59–78.
  • Lighthill J. (1981):, Energy flow in the cochlea. — J. Fluid Mech., Vol.106, pp.149–213.
  • Lions J.-L. (1988): Exact controllability, stabilization and perturbations for distributed systems. — SIAM Rev. Vol.30, No.1, pp.1–67.
  • Lions J.-L. and Zuazua E. (1995): Approximate controllability of hydro-elastic coupled system. — ESAIM: Contr. Optim. Calc. Var., Vol.1, pp.1–15.
  • Micu S. and Zuazua E. (1997): Boundary controllability of a linear hybrid system arising in the control of noise. — SIAM J. Contr. Optim., Vol.35, No.5, pp.1614–1637.
  • Necas J. (1967): Les Méthodes directes en théorie des équations elliptiques. — Paris: Masson.
  • Osses A. and Puel J.-P. (1998): Boundary controllability of a stationary stokes system with linear convection observed on an interior curve. — J. Optim. Theory Appl., Vol.99, No.1, pp.201–234.
  • Osses A. and Puel J.-P. (1999): Approximate controllability for a linear model of fluid structure interaction. — ESAIM Contr. Optim. Calc. Var., Vol.4, No.??, pp.497–519.
  • Pazy A. (1983): Semigroups of Linear Operators and Applications and Partial Differential Equations. — New York: Springer-Verlag.

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Bibliografia

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