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Tytuł artykułu

Controllability of the Semilinear Heat Equation with Impulses and Delay on the State

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we prove the interior approximate controllability of the following Semilinear Heat Equation with Impulses and Delay [...] where Ω is a bounded domain in RN(N ≥ 1), φ : [−r, 0] × Ω → ℝ is a continuous function, ! is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ! and the distributed control u be- longs to L2([0, τ]; L2(Ω; )). Here r ≥ 0 is the delay and the nonlinear functions f , Ik : [0, τ] × ℝ × ℝ → ℝ are smooth enough, such that [...] Under this condition we prove the following statement: For all open nonempty subset ! of Ω the system is approximately controllable on [0, τ], for all τ > 0.
Wydawca
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2015-05-20
zaakceptowano
2015-08-15
online
2015-10-16
Twórcy
autor
  • Leiva: Louisiana State University, College of Science, Math. Department, Baton Rouge, LA 70803-USA
Bibliografia
  • ---
  • [1] N. Abada, M. Benchohra and H. Hammouche, Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay,CUBO A Mathematical Journal Vol. 02, (1-17). june 2010.
  • [2] H. Akca, a. Boucherif and V. Covachev, Impulsive Functional-Differential Equations with Nonlocal Conditions, IJMMs 29:5 (2002) 251-256.
  • [3] A.E. Bashirov and Noushin Ghahramanlou, On Partial Approximate Controllability of Semilinear Systems. COGENTENG- Engeneering, Vol. 1, 1-13 (2014), doi: 10.1080/23311916.2014.965947 [Crossref]
  • [4] A.E. Bashirov and Noushin Ghahramanlou, On Partial Complete Controllability of Semilinear Systems. Abstract and Applied Analysis, Vol. 2013, Article ID 52105, 8 pages. [WoS]
  • [5] A.E. Bashirov, N. Mahmudov, N. Semi and H. Etikan, No On Partial Controllability Concepts. Inernational Journal of Control, Vol. 80, No. 1, January 2007, 1-7.
  • [6] D. N. Chalishajar, Controllability of Impulsive Partial Neutral Funcional Differential Equation with Infinite Delay. Int. Journal of Math. Analysis, Vol. 5, 2011, No. 8, 369-380.
  • [7] D.Barcenas, H. Leiva and Z. Sivoli, A Broad Class of Evolution Equations are Approximately Controllable, but Never Exactly Controllable. IMA J. Math. Control Inform. 22, no. 3 (2005), 310–320.
  • [8] K. Balachandran and J. H. Kim, Remarks on the Paper Controllability of Second Order Differential Inclusion in Banach Spaces, (J. Math. Anal. Appl.) J. Math. Anal. Appli. 324 (2006), 746-749. [Crossref]
  • [9] Lizhen Chen and Gang Li, Approximate Controllability of Impulsive Differential Equations with Nonlocal Conditions. Inter- national Journal of Nonlinear Science, Vol.10(2010), No. 4, pp. 438-446.
  • [10] R.F. Curtain, A.J. Pritchard, Infinite Dimensional Linear Systems. Lecture Notes in Control and Information Sciences, 8. Springer Verlag, Berlin (1978).
  • [11] R.F. Curtain, H.J. Zwart, An Introduction to Infinite Dimensional Linear Systems Theory. Text in Applied Mathematics, 21. Springer Verlag, New York (1995).
  • [12] V. Lakshmikantham, D. D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
  • [13] H. Leiva, N. Merentes and J. Sanchez "A Characterization of Semilinear Dense Range Operators and Applications", to appear in Abstract and Applied Analysis.
  • [14] H. Leiva, N. Merentes and J. Sanchez “Interior Controllability of the Benjamin-Bona-Mahony Equation”. Journal of Mathe- matis and Applications, No. 33,pp. 51-59 (2010).
  • [15] H. Leiva, N. Merentes and J. Sanchez “Interior Controllability of the Semilinear Benjamin-Bona-Mahony Equation”. Journal of Mathematis and Applications, No. 35,pp. 97-109 (2012).
  • [16] H. Leiva, N. Merentes and J. Sanchez “Approximate Controllability of a Semilinear Heat Equation”. Interntional Journal of Partial Differential Equations Mathematis,Vol. 2013, Art. ID 424309, 7 pages.
  • [17] Hugo Leiva, Approximate Controllability of Semilinear Impulsive Evolution Equations, Abstract and Applied Analysis, Vol. 2015, Article ID 797439, 7 pages [WoS]
  • [18] A. M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations. World Scientific Series on Nonlinear Science Series A, Vol. 14, 1995.
  • [19] A. Carrasco, Hugo Leiva, J.L. Sanchez and A. Tineo M, Approximate Controllability of the Semilinear Impulsive BeamEquation with Impulses. Transaction on IoT and Cloud Computing 2(3) 70-88, 2014.
  • [20] Hugo Leiva, Controllability of Semilinear Impulsive Nonautonomous Systems, International Journal of Control, 2014, http/dx.doi.org/10.1080/00207179.2014.966759. [Crossref][WoS]
  • [21] Hugo Leiva and N. Merentes,Approximate Controllability of the Impulsive Semilinear Heat Equation. Journal of Mathematics and Applications, No. 38, pp 85-104 (2015)
  • [22] S. Selvi and M. Mallika Arjunan, Controllability Results for Impulsive Differential Systems with Finite Delay J. Nonlinear Sci. Appl. 5 (2012), 206-219.
  • [23] R. Shikharchand Jain and M. Baburao Dhakne, On Mild Solutions of Nonlocal Semilinear Impulsive Functional Integro- Differential Equations, Applied Mathematics E-Notes, 13(2014), 109-119.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_msds-2015-0004
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