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Finite extinction and null controllability via delayed feedback non-local actions

Díaz Díaz, Jesús Ildefonso and Casal, A.C. and Vegas Montaner, José Manuel (2009) Finite extinction and null controllability via delayed feedback non-local actions. Nonlinear analysis-theory methods & applications, 71 (12). pp. 2018-2022. ISSN 0362-546X

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We give sufficient conditions to have the finite extinction for all solutions of linear parabolic reaction-diffusion equations of the type partial derivative u/partial derivative t - Lambda u = -M(t)u(t - tau, x) (1) with a delay term tau > 0, on Omega, an open set of R(N), M(t) is a bounded linear map on L(p)(Omega), u(t, x) satisfies a homogeneous Neumann or Dirichlet boundary condition. We apply this result to obtain distributed null controllability of the linear heat equation u(t) - Delta u = upsilon(t, x) by means of the delayed feedback term upsilon(t, x) = -M(t)u(t - tau, x).

Item Type:Article
Uncontrolled Keywords:Finite extinction time; Delayed feedback control; Linear parabolic equations
Subjects:Sciences > Mathematics > Numerical analysis
ID Code:15071

E. Winston, J.A. Yorke, Linear delay differential equations whose solutions become identically zero, Rev. Roumaine Math. Pures Appl. 14 (1969) 885_887.

J.K. Hale, Theory of Functional Differential Equations, Springer, New York, 1977.

A. Casal, J.I. Diaz, J.M. Vegas, Finite extinction time via delayed feedback actions, Dyn. Contin. Discrete Impuls. Syst. Ser. A S2 (2007) 23_27.

S Antontsev, J.I. Díaz, S. Shmarev, Energy Methods for Free Boundary Problems. Applications to Nonlinear PDEs and Fluid Mechanics, Birkäuser, Boston, 2002.

K.S. Ha, Nonlinear Functional Evolutions in Banach Spaces, Kluwer, AA Dordrecht, 2003.

M.N. Özisik, Boundary Value Problems of Heat Conduction, Dover, New York, 1989.

I. Stakgold, Green's Functions and Boundary Value Problems, second edition, Wiley, New York, 1998.

A. Friedman, M.A. Herrero, Extinction properties of semilinear heat equations with strong absorption, J. Math. Anal. Appl. 124 (1987) 530_546.

C.V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum, New York, 1992.

I.I. Vrabie, C0-Semigroups and Applications, North-Holland, Amsterdam, 2003.

Deposited On:03 May 2012 08:45
Last Modified:06 Feb 2014 10:15

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