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Approximate controllability of semilinear impulsive strongly damped wave equation

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Rothe’s fixed-point theorem is applied to prove the interior approximate controllability of a semilinear impulsive strongly damped wave equation with Dirichlet boundary conditions in the space Z1/2 = D((-Δ)1/2) × L2(Ω), where Ω is a bounded domain in Rn (n ≥ 1). Under some conditions we prove the following statement: For all open nonempty subsets ω of Ω the system is approximately controllable on [0, τ]. Moreover, we exhibit a sequence of controls steering the nonlinear system from an initial state z0 to a neighborhood of the final state z1 at time τ > 0.
Wydawca
Rocznik
Strony
45--57
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
autor
  • Dpto. de Sistemas de Control, Facultad de Ingeniería, Universidad de Los Andes, Mérida 5101, Venezuela
autor
  • Dpto. de Sistemas de Control, Facultad de Ingeniería, Universidad de Los Andes, Mérida 5101, Venezuela
autor
  • Department of Mathematics, Missouri State University, Springfield, MO 65897, USA
autor
  • Dpto. de Sistemas de Control, Facultad de Ingeniería, Universidad de Los Andes, Mérida 5101, Venezuela
Bibliografia
  • [1] D. D. Bainov, V. Lakshmikantham and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientic, Singapore, 1989.
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  • [6] L. Chen and G. Li, Approximate controllability of impulsive differential equations with nonlocal conditions, Int. J. Nonlinear Sci. 10 (2010), no. 4, 438–446.
  • [7] S. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems, Pacific J. Math. 136 (1989), no. 1, 15–55.
  • [8] R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems, Lecture Notes in Control and Inform. Sci. 8, Springer, Berlin, 1978.
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  • [10] G. Isac, On Rothe’s fixed point theorem in general topological vector space, An. Stiint. Univ. “Ovidius” Constanta 12 (2004), no. 2, 127–134.
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  • [19] H. Larez, H. Leiva and J. Rebaza, Approximate controllability of a damped wave equation, Can. Appl. Math. Q. 20 (2012), 405–419.
  • [20] H. Leiva, A lemma on C0-semigroups and applications, Quaest. Math. 26 (2003), 247–265.
  • [21] H. Leiva, N. Merentes and J. Sanchez, Interior controllability of the Benjamin-Bona-Mahony equation, J. Math. Appl. 33 (2010), 51–59.
  • [22] H. Leiva, N. Merentes and J. L. Sanchez Approximate controllability of semilinear reaction diffusion, Math. Control Relat. Fields 2 (2012), no. 2, 171–182.
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Typ dokumentu
Bibliografia
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